October 2007

Secretary/Principal Immigration Officer, Collector of Customs andImmigration Officer.4.4 One of the first tasks of the group was to consider a draft immigration policystatement as follows:The Falkland Islands Immigration Policy seeks to encourage, on a gradual andcontrolled basis, such permanent immigration as is in the interests of theFalkland Islands, taking account of the need:(a) To increase the human capital of knowledge, ability and skill in theFalkland Islands;(b) To develop and increase enterprise and innovation in the Falkland Islands;and(c) To safeguard social cohesion and promote integration in the FalklandIslands4.5 This draft policy statement was presented to Executive Council on 27 th April2006 as providing broad parameters for the development of an immigrationpoints system and was a reworded version of the paragraph regarding thepurpose of the issue of Permanent Resident Permits contained in the originalSection 18 (5) of the Immigration Ordinance 1999.4.6 An immigration points system was subsequently developed and approved byExecutive Council in 2009. However it was intended that further work wouldbe required to consider the assessment of special categories of persons e.g.investors.4.7 The points system is based on a number of criteria for which points areawarded, including qualifications and finances. The points system came intoeffect in October 2009. Following this process, a number of issues were raisedby applicants and Members of the Legislative Assembly regarding the criteriaused within the points system.4.8 Against the background of an absence of policies and systems to support theexisting Immigration framework, and the concerns expressed by Members inconnection with the points system, it is clear that there is a need to undertake acomprehensive review of immigration policy, beginning with a review of thefundamental policy statement (paragraph 4.4 above), to ensure thatimmigration policy meets the current and future needs of the Falkland Islands.4.9 Members have therefore requested a Strategic Review of Immigration whichwill be coordinated by the Principal Immigration Officer.

Research Works done at NCTS are in thedirection of Conformal field theory, StringTheory, Nonlinear Partial DifferentialEquations from models in Physics, relatedScientific Computations, etc. Another areawhich NCTS has made considerable endeavoris Mathematical Biology and BiologicalPhysics and System Biology. Our majordirections in math biology is populationdynamics, and bioinformatics. We have builtup interdisciplinary teams in both directions,interacting constantly with experts in relatedfields of biological sciences. They alreadyproduced series of very significant researchresults in important international journals ofrelated subjects. In particular, the developmentof bioinformatics at NCTS is greatly helpedby Academician Wen-Hsiung Li from theUniversity of Chicago.Due to eye pressure problem, the Head ofPhysics Division, Professor Hsiang-nan Lihad to resign in July 2007. We have askedProfessor Chung-Yu Mou from NationalTsing-Hua University to serve as the new headof Physics Division starting from August 1,2007. Also Professor Chon-Saar Chu fromNational Chiao-Tung University has kindlyagreed to serve as deputy head of the PhysicsDivision. We are extremely grateful toProfessor Hsian-nan Li for his excellentservices to NCTS in the year 2006/2007.Finally the mathematics Division has alsoappointed two deputy heads starting fromAugust 1, Professor Wen-Wei Lin fromNTHU and Professor Yuan-Chung Sheu fromNCTU.Another enlightening development atNCTS is the establishment of YoungTheorists Awards. The aim is to encourageyoung colleagues to pursue theoreticalresearches, to maintain active and to doexcellent works. The selection of recipients isbased on evaluations from internationalexperts. There are four recipients in 2007,Chih-Tin Shih of Tung-Hai University, andDaw-Wei Wang of NTHU in Physics, Kuo-Chang Chen of NTHU and Cheng-HsiungHsu of NCU in mathematics. The tworecipients in mathematics later on have alsobeen awarded 2007 Ta-You Wu Fellowship ofNSC. NCTS is promised to be a breedingground for next generation theoreticalscientists in Taiwan, we shall keep thispromise.Words from the Director -›› 2

Mathematics Division

Report of the Division HeadCTS started its operation on August 1,1997. It is already ten years old. Weare very happy to have our 10-th yearanniversary celebration this summer, withAcademician Shing-Tung Yau from HarvardUniversity visited us at August 1 2007, for oneweek. Professor Yau has been chairman of ourinternational advisory committee inmathematics since 10 years ago. Also joiningus this summer at NCTS are the academicians,Professor Horng-Tzer Yau, Professor Yum-Tong Siu, both from Harvard University, andProfessor Wen-Hsiung Li from the Universityof Chicago. Professors H.-T. Yau and W.-H. Lihave also been on our advisory committee, andmade constant advices to us during theseyears. There are many other old friends inmathematics coming to see us this summer,and we are grateful to all of them for their longterm enthusiastic and devoted efforts to helpand support NCTS growing up.Starting from the second phase of operation(January 2004), the hosting universities of themain project of NCTS, i.e. NTHU and NCTU,promised to raise the offer of center scientistspositions, from 4 positions to 10 positions inMathematics. The center scientists are veryimportant to the actual operation of the center,they reside at NCTS leading the researches ofthe various topical programs. We are satisfyingto report that from August 1 this very year, weget ten Center Scientists in Mathematics forthe first time. They are: Guan-Yu Chen(NCTU) in Probability, Jiun-Cheng Chen(NTHU) in Algebraic Geometry, Kuo-ChangChen (NTHU) in Dynamical System, Ment-Kiat Chuah (NTHU) in Representation Theory,Ming-Chia Li (NCTU) in Dynamical system,Song-Sun Lin (NCTU) in Dynamical System,Wen-Hsiung Lin (NTHU) in Topology, Dong-Ho Tsai (NTHU) in Differential Geometry,Chin-Lung Wang (NCU) in AlgebraicGeometry, Jing Yu (NTHU) in NumberTheory. To make the operations at Hsinchumore effective, the Mathematics Division alsoappointed two Deputy Heads at August 1:Professor Wen-Wei Lin from NTHU andProfessor Yuan-Chung Sheu from NCTU.We are also continuing our commitment tosupporting younger generation as much as wecan. This year we have partially supported 6Ph.D. students, to ICTP summer school inItaly, Arizona winter school in USA, MSRIworkshop in USA, and presenting paper atjournees arithmetiques in Britain. We alsosupported 4 post doctors and junior faculties tointernational conferences/workshops. We grantCTS fellowships to one junior faculty visitingCornell University/Georgia Tech, and onePh.D. student doing research at QueensUniversity, both for period of three months.There are more than 50 students enrolled inout summer internship program.As before, the NCTS 2007 Math PreprintSeries is divided into three subseries I, II, andIII, collected from the main project and thetwo subprojects respectively. Works fromNCTS preprint series of past years haveappeared in various important internationalmathematical journals, including the mostinfluential ones. For example, the paper byYuan-Pin Lee, Hui-Wen Lin (NCU), and Chin-Lung Wang (NCU), entitled : Flops,Correspondences and Quantum Correctionshas now been accepted by the Annals ofMathematics. We have reported this importantprogress of algebraic geometry last yearalready in the NCTS 2006 Annual Report.This annals paper is just the beginning of aReport of the Division Head -›› 4

eak through in higher-dimensional geometrymade by these authors after years of study andcollaborations supported by NCTS. Y.-P. Leeis a frequent visitor to NCTS from Utah forseveral years.Looking at the works reported by ourvarious topical programs this year, I wouldlike to comment particularly on resultsobtained by several international long termcollaborations. From the south of Taiwan,Ching Hung Lam at NCKU is an expert onVertex Operator Algebras, this is in the frontierof algebra which is interwoven withmathematical physics. Lam and H. Yamauchiof Tsukuba made progress since 2005 onstructures of framed operator algebras andtheir orbifolds, their preprints have beenaccepted by important journals such asCommunications in Mathematical Physics.Around the same time, Lam , with C. Dongand R. L. Greiss from the US, also obtained aninteresting characterization of the famousMoonshine vertex operator algebra. This workhas just been published by American Journalof Mathematics.Calabi-Yau threefold has been at the centralstage of mathematics since two decades ago. Itinvolves algebraic geometry, string theory, andmore recently arithmetic geometry. In 2004Yifang Yang of NCTU visited N. Yui ofCanada, under support of NCTS, they have asuccessful collaboration ever since, on themonodromy of hypergeometric differentialequations which leads, among other things, toa fascinating paper on Picard-Fuch differentialequations and Calabi-Yau threefolds. Thispaper is now accepted by the Crelle Journal.Another coauthor of this important work isYang's Ph. D. student Yao-Han Chen who didmost of the complicate but essentialcalculations.Another important paper in 2007 NCTSpreprint series is: Algebraic independence ofCarlitz zeta values for different constant fields,by Chieh-Yu Chang, M. A. Papanikolas andJing Yu. Chang is currently a post doctor atNCTS. This collaboration started in summer2004 when Papanikolas visited NCTS fromTexas. The results in a series of break throughin transcendence theory over function fields.Papanikolas' first work in this series has beenaccepted by inventione mathematicae, Chang-Yu's first work in this series just appears inAdvances in Mathematics. The preprint inquestion is the 2nd in the series, which provesthat for rational function field over finiteconstant fields, all the algebraic relationsamong the zeta values at positive integerscome from the Euler-Carlitz relations and theFrobenius relations.Non-linear partial differential equations istraditionally a strong research area in Taiwan.The focus group at NTU Chang-Shou Lin,Chiun-Chuan Chen, Tai-Chia Lin amongothers, have been very productive in recentyears, with many first rate papers coming out.C.-S. Lin has long term collaboration withMax-Plank group at Leipzig, G. Wang and J.Yost in particular. Their recent important workon analytic aspects of Toda's system hasappeared recently in Communications on Pureand Applied Mathematics. T.-C. Lin has beencollaborating successfully with J.F. Wei ofCHUK in recent years on spike solution ofcoupled nonlinear Schrödinger equations, withresults published by e.g. Annales de L'institutHenri Poincaré, Communications inMathematics Physics, Nonlinearity. Anotherimportant paper which appeared this year inJournal of Functional Analysis, is by C.-S.Lin, A. C. Ponce and Yisong Yang, in it is aproof of the very interesting existence oftopological vortices in a relativistic self-dualAbelian Chern-Simons theory with two Higgsparticles and two gauge fields.The above describes samples of the bestworks done at NCTS. There are certainly otherimportant works at the center. Entering itssecond ten years, mathematicians at NCTS areready to make further progress and toaccomplish greater achievements in research.5 ‹‹- Report of the Division Head

Executive Committee MembersCommitteesChiun-Chuan ChenI-Liang ChenGerard J. ChangWen-Wei LinChin-Lung WangSoon-Yi WuJing YuAffiliationNational Taiwan UniversityNational Taiwan UniversityNational Taiwan UniversityNational Tsing Hua UniversityNational Central UniversityNational Cheng Kung UniversityNational Tsing Hua UniversityExecutive Committee Members -›› 6

Academic Committee MembersCommitteesGerard J. ChangJung-Kai ChenShun-Jen ChengLiang-Chung HsiaSze-Bi HsuMing-Chih LaiYng-Ing LeeSong-Sun LinTai-Chia LinYuen-Chung SheuSoon-Yi WuWei-Cheng WangJing YuAffiliationNational Taiwan UniversityNational Taiwan UniversityNational Taiwan UniversityNational Central UniversityNational Tsing-Hua UniversityNational Chiao Tung UniversityNational Taiwan UniversityNational Chiao Tung UniversityNational Taiwan UniversityNational Chiao Tung UniversityNational Cheng Kung UniversityNational Tsing Hua UniversityNational Tsing Hua University7 ‹‹- Academic Committee Members

Highlights of the ProgramsD.1 Algebraic Geometry at NCTS 2004-2007Coordinator: Hui-Wen Lin (National Central University)Part I: People and Activitieshe goal of NCTS algebraic geometryprogram is to promote fundamentalresearches, to attract young talented studentsto study it and to bring up frontier researchproblems such that domestic researchers aswell as foreign visitors can work together onthem through regular activities. To achieve thisgoal, we ran two types of activities during2004-2007. The first type is for students,which includes weekly student's seminars,winter courses and summer courses. Thesecond type is purely for research purpose,which includes the weekly research seminar,advanced courses, summer schools andworkshops.There were over 50 short term visitorsjoining in NCTS algebraic geometry programduring 2004-2007. Among them are eithersenior scholars of great renown such as H.Esnault, E. Getzler, Y. Kawamata, J.McKernan, S.Mukai, . R. Pandharipande, M.Reid, Yum-Tong Siu, E.Viehweg, Kang Zuo orpromising young algebraic geometers such asC. Birkar, P. Cascini, C.D. Hacon, Yuan-PinLee, Xiaotao Sun, Sheng-Li Tan etc. We arepleased to mention that C. Birkar, P. Cascini,C. D. Hacon and J. McKernan had a joint workto make a very big break-through on higherdimensional Minimal Model Program (MMP)last year. All of them individually reported thisremarkable work in the NCTS workshops orthe NCTS summer school from variousviewpoints during 2004-2007. Many domesticresearchers and students got the up-to-dateresearch information from these talks and hadthe chance to discuss the related problems withthem. We believe that it will stimulatefundamental research growth here in thefollowing years.People involved in NCTS algebraicgeometry program consist of local researchers,foreign visiting scholars, research assistantsand visiting graduate students.Local Researchers• Jungkai A. Chen (NTU)• Jiun-Cheng Chen (NCTS frequent visitorand Northwestern University (2004 - 2006),NCTS center scientist and NTHU (2006-)• Hui-Wen Lin (NCTS postdoctor (2000-2001), NCU(2001-)• Chin-Lung Wang (NCTS center scientist andNCU)• Hung-Jen Chiang-Hsieh (NCTS postdoctor(2003-2004), CCU(2004-)• Jyh-Haur Teh (NCTS postdoctor (2005-2006), NTHU(2006-)• Yen-Lung Tsai (NCTS postdoctor (2004-2005), NCCU(2005-)Highlights of the Programs -›› 8

Frequent Visitors• The following scholars keep workingtogether with some local researchers (Y.-P.Lee with H.-W. Lin and C.-L.wang; H.-H.Tseng with J.-C.Chen).• Yuan-Pin Lee (University of Utah)• Hsian-Hua Tseng (University of BritishColumbia)Short Term VisitorsF. Ambro (RIMS), D. Andrea (Padova), C.Birkar (Cambridge), P. Cascini (UC SantaBarbara), C.-L. Chai (U. of Penn and NCTS),M. Chen (Fudan U.), I. Ciocan-Fontanine(Minnesota), A.Corti (Cambridge), L. Ein(Illinois), H. Esnault (Essen), E. Getzler(Northwestern), G. Farkas (Princeton),Tommaso de Fernex (Utah), O. Fujino (IASand Nagoya), C. Hacon (Utah), J.-M. Hwang(KIAS), M. Kawakita (Tokyo), Y. Kawamata(Tokyo), S. Kebekus (Bayreuth), J. Keum(KIAS), B. KIM (KIAS), S. Kovacs(Washington), A. Kresch (Warwick), J.M.Landsberg (Georgia Tech /Texas A.M.), W.-P.Li (HKU of S.T.), S. Lu (Essen), J. McKernan(UC Santa Barbara), M. Mella (Ferrara), N.Mok (HKU), S. Mukai (RIMS Kyoto), K.Oguiso (Toyko), R. Pignatelli (Trento), R.Pandharipande (Princeton), M. Paun(Strasbourg), T. Peternell (Bayreuth), M. Popa(Harvard), Z. Ran (California Riverside), M.Reid (Warwick), P. Schapira (dierre et marieCurie), S. Schroer (Bayreuth), B. Siebert(Freiburg), Y.-T. Siu (Harvard), X.-T. Sun(Academia Sinica of China and HKU), S.-L.Tan (Essen and East China Normal U.), Z.Tang (Suzhou U.), J. Tilouine (Paris-Nord), A.Todorov (UC Santa Cruz), Y.-L. Tong(Purdue), G.R. Vasant (Tata Institute), E.Viehweg (Essen), J. Wierzba (EnergyConvergence Group), J. Wlodarczyk (Purdue),T. Yasuda (Kyoto), Stephen S.-T. Yau(Illinois), D.-Q. Zhang (Singapore), I. Zharkov(Harvard), J. Zhou (Beijin Tsing-Hua U.), K.Zuo (Mainz).Research Assistants• Keng-Li Lin (NCTS RA (2003-2004), NCU(2004-))• Jen-Yuin Lin (NCTS RA (2004-2005),Columbia U. (2005-))• Kung-Zen Wu (NCTS RA (2004-2005)• Yu-Shen Lin (NCTS RA (2006-2007),Harvard U. (2007-))Visiting Graduate Students• Chen-Yu Chi (Harvard)• Yu-Chieh Chung (Utah)• Ming-Tao Chuan (Harvard)• C.-C. Liu (UCLA)• Yu-jong Tzeng (Stanford)Student's ProgramThere are three purposes for the student'sprogram during 2004-2007. The fist one is toprepare the background for students who wereselected to participate in "Asia – FrancoSummer School in Algebraic Geometry:Motives and related topics", held by IHESfrom 2006 July 15 to 30. The second one is toprepare the background of MMP for studentswho were interested in the fruitful activitiesrelated to MMP at NCTS. The third one is toprovide students background for advancedstudy in Mirror Symmetry and other relatedtopics.For the First Purpose• The winter course in basic projectivegeometry was organized by H.-W. Lin andheld at NCU in 2005.• The winter course in Lie Algebras wasorganized by C.-L. Wang in 2005.• The summer course in complex algebraicgeometry was organized by H.-W. Lin in2005.• The weekly student seminar in etalecohomology was organized by H.-W. Linand C.-L. Wang from 2006 March to June atNCU.For the Second Purpose• A regular student seminar was organized byJ.A. Chen and held at NTU from 2005 to2007. .• NCTS summer lecture series on intersection9 ‹‹- Highlights of the Programs

theory and Riemann-Roch theorem wasgiven by V. Maillot and held at NTU in2005.For the Third Purpose• A student seminar on basic algebraicgeometry was organized by J.-C. Chen inJuly 2006.• C.-L. Wang organized some student seminarsregularly at NCTS or at NCU from 2004 to2007.Research ProgramsNCTS keeps running high standardactivities in algebraic geometry. We choose thetopics directly related to our research interestincluding• Birational Geometry, especially the newdevelopment in the Minimal Model Programby Shokurov, Siu and Biakar-Cascini-Hacon-McKernan• The theory of K-equivalence and relatedtheory on Quantum Cohomology• The theory of Calabi-Yau manifolds andMirror SymmetrySeminars in Algebraic Geometry• Many short courses in Gromov-Wittentheory were given by Y.-P. Lee from 2004 to2006.• Regular research seminars were organized byC.-L. Wang at NCTS and by J.A. Chen atNTU from 2004 to 2007. The maincontributors included J.A. Chen, J.-C. Chen,H.-W. Lin, C.-L. Wang and some short termvisitors.Advanced Courses• The advanced course on Flips, Mori fiberspaces and Mirror symmetry of Fano 3-foldswas given by A.Corti at NTU from 2004January to March.• NCTS 2005 summer course in HomologicalAlgebra and D-modules was lectured byAndrea D'Agnolo and P. Schapira at NTU.• The Mini-Course in recent development ofminimal model theory was given by Y.Kawamata at the end of 2005 at NTU andNCU.Summer Schools• 2004 NCTS Summer School in AlgebraicGeometry (22-26 June; 5-9 July).• Organizers: J.A. Chen, Y.-P. Lee, E. Viehwegand C.-L. Wang• Speakers: A. Corti, L. Ein, H. Esnault, S.Kebekus, M. Paun, R.Pandharipande, Z. Ran, E.Viehweg• Topics: Gromov-Witten theory, rationalcurves and higher dimensionalbirational geometry• 2005 NCTS Summer School in AlgebraicGeometry (8-18 August).• Organizers: C.-L. Wang• Speakers: A. Todorov, Kang Zuo, Jian Zhou,C.-L. Wang• Topics: the geometry of moduli spaces,methods of localization in stringdualities and birational geometry.• 2007 NCTS Mini-Course in AlgebraicGeometry (3-12 July).• Organizers: J.A. Chen, J.-C. Chen and C.-L.Wang• Speakers: C. Birkar, J.A. Chen, P. Cascini,M. Kawakita• Topics: the latest development of higherdimensional MMPWorkshops• 2004 Workshop on Higher DimensionalAlgebraic Geometry (22-28 March) at NTUwas organized by A. Corti, M. Reid and J.A.Chen. The purpose of this workshop is tostudy the development of higher dimensionalMMP and related topics such as linear series,K-equivalence and some analytic aspects.• 2004 NCTS Workshop in AlgebraicGeometry (28 June-2 July) was organized byJ.A. Chen, Y.-P. Lee, E. Viehweg and C.-L.Wang. The main theme is on Gromov-Wittentheory, rational curves and higherdimensional birational geometry.• 2006 NCTS Workshop in AlgebraicHighlights of the Programs -›› 10

Geometry (7-12 July) was organized by Y.-P.Lee. The main purpose is to study Deligne-Mumford moduli spaces of stable curves andGromov-Witten theory. The main speaker isE. Getzler.• 2007 Workshop on Higher DimensionalAlgebraic Geometry (27-31 March) at NTUwas organized by J.A. Chen, J.-C. Chen andC.-L. Wang. The purpose of this workshop isto study the development of higherdimensional algebraic geometry includingMMP, singularity theory, toric theory andflops.Part II. Accomplishments andAnticipationsSelected works of local researchers:[1] J.A. Chen, C.D. Hacon, Varieties with P 3 =4and q=dim X, Ann. Sc. norm. super. Pisa,V, vol. III. (2004), 399-425.[2] J.A. Chen, M. Chen, D.Q. Zhang, The 5-canonical system on 3-folds of generaltype, J. Reine Angew. Math., 603, (2007),165-181.[3] J.A. Chen, C.D. Hacon, Pluricanonicalsystems on irregular 3-folds of generaltype, Math. Zeit, 255, (2007), 343-355.[4] D. Abramovich , J.-C. Chen, Flops, flipsand perverse point sheaves on threefoldstack, J. Algebra 290 (2005), no. 2, 372-407.[5] J.C. Chen, H.H. Tseng, Cone theorem viaDeligne-Mumford stacks, Preprintmath.AG 0505043, submitted to J.Algebraic Geometry, 2005.[6] J.-C. Chen, H.-H. Tseng, Note oncharacterizations of projective spaces, toappear in Comm. Algebra.[7] Y.-P. Lee, H.-W. Lin, C.-L. Wang, Flops,motives and invariance of quantum rings,to appear in Annals of Mathematics.For the passed twenty five years, the MMPdeveloped by Mori in 1982 and by others(Kawamata, Kollar, Shokurov etc) in thesequel has been the core theory in higherdimensional algebraic geometry. In 1988, Morisolved the flip conjecture in dimension 3 andachieved the 3-dimensional MMP. He thenreceived the 1990 Fields Medal due to thisfundamental work. However, to get theexistence of higher dimensional minimalmodels and to understand the non-uniquenessissues of minimal models are still challengingproblems. C.-L. Wang in 1998 initiated thenotion of K-equivalence aiming at resolvingthe non-uniqueness problem.C.-L. Wang in 1998 showed that K-equivalent smooth varieties have the sameBetti numbers. In 2006, Y.-P. Lee, H.-W. Linand C.-L. Wang [7] showed that for ordinaryflops, the graph closure gives rise to thecanonical isomorphism of Chow motives inthe sense that the Poincare pairing is preservedunder the correspondence. Ordinary flops arenot only the first examples of K-equivalentmaps, but also crucial to the general theory.However the cohomology ring structures are ingeneral different. They precisely determinedthe defect caused by the classical productunder simple ordinary flops and found thisdefect is exactly remedied by adding thequantum corrections attached to the extremalrays. For simple ordinary flops, they showedthat the big quantum cohomology ring isinvariant after an analytic continuation overthe extended Kahler moduli spaces. Thisanalytic continuation phenomenon is theirmajor contribution to the study of higherdimensional algebraic geometry.In [4], D. Abramovich and J.-C. Chen madesome contribution in understanding flops andflips in terms of derived categories and modulispaces: they generalized Bridgeland's result toterminal Gorenstein threefolds flops andproved similar results for threefold Franciaflips. In [5], J.-C. Chen and H.-H. Tsengworked out important results in Cone theormin characteristic p as well as sharp estimate oflength of extremal rays for LCIQ (quotient oflocally complete intersection singularities)varieties. They combine moduli of stackystable maps with Mori's bend and break theoryand open a research direction. An interestingapplication is their characterization results ofprojective spaces for possibly singular11 ‹‹- Highlights of the Programs

varieties [6].The research of J.A. Chen was mainlyaround the birational classification problem.For varieties of general type, mK defines abirational map for m sufficiently large. It'snatural to ask whether one can determine meffectively. For dim X =1, 2, these bounds areknown to be 3 and 5 respectively. There is arecent work by Hacon and McKernan assertsthat there is a theoretical bound m(n) whichdepends on dim X = n. However, the numberm(n) is far from being optimal in any way. Onhis joint work with Meng Chen and De-QiZhang [2], they obtained that 5K is birationalfor minimal Gorenstein threefolds with atworst canonical singularities. This bound isoptimal. In [1], they could completely describevarieties with P 3 ≤ 4 and q = dim X. In [3],they proved that if X is an irregular 3-fold withsome positivity, then |mK| is birational for allm bigger than or equal to 5.NCTS Post-doctors in AlgebraicGeometryWe would like to mention that since 1997,all NCTS post-doctors working on algebraicgeometry got the teaching positions in nationalresearch universities one after another. We listtheir works (for people after 2004) as follows.[1] H.-J., Chiang-Hsieh and J. Lipman, Anumerical criterion for simultaneousnormalization, Duke Math. J. 133 (2006),no. 2, 347-390.[2] J.-H. Teh, Complexification of real cyclesand Lawson suspension theorem, J.London Math., 75 (2007), 463-478.[3] J.-H. Teh, Harnack-Thom theorem forhigher cycle groups and Picard varieties, toappear in the Transaction of AMS.[4] Y. L. Tsai and E. Z. Xia. Non-abelian localinvariant cycles. Proc. Amer. Math.Soc.135 (2007), No.8, 2365-2367.AnticipationsIn the future, we will keep on organizinghigh standard activities for cultivating studentsas well as stimulating research works, and tryto open up more channels to collaborate withreputable foreign visitors. Meanwhile, we arestill focusing on promoting researches relatedto birational geometry including MMP, Calabi-Yau manifolds and Mirror symmetry, as wellas motivic or quantum-theoretic aspects ofalgebraic geometry. In particular, the currentremaining step to complete the MMP in higherdimensions is the termination conjecture offlips. To resolve this conjecture may requirenew invariants for singular varieties. We willbe interested in studying it by combining theclassic minimal model theory with othertechniques from orbifold theory, arc spaces,quantum cohomology as well as the theory ofmotives.Since 2000, there have been manyoutstanding students from NCTS studyingalgebraic geometry in the top rankinguniversities of U.S.A. We expect that they willjoin our research group to enhance theresearch works in a few years.Highlights of the Programs -›› 12

D.2 Discrete Mathematics at NCTS 2004-2007Coordinator: Gerard Jennhwa Chang (National Taiwan University) and Xuding Zhu (National Sun Yat-sen University)Part I: Background and Activities inthe Programiscrete mathematics has seen rapiddevelopment in recent decades, bothabroad and in Taiwan, in width and in depth.As a focus group of NCTS, the discretemathematics group has been focused onresearch in graph coloring, graph labeling,combinatorial optimization, algorithms,enumerative combinatorics, clustercombinatorics, combinatorial number theory.In the past four years, through seminars,workshops and hosting visitors, the project hashelped local focus group, especially youngresearchers in the group, to establishcollaborations with researchers abroad,develop links with experts abroad, and starttheir research in the frontier of related fields.Discrete mathematics program in NCTShas two teams, one in north which is organizedby by Gerad Jennhwa Chang at NationalTaiwan University, the other in south which isorganized by Xuding Zhu at National Sun YatsenUniversity.During the past four years, the discretemathematics group in north has invited 6visitors. As we do not have budge for postdoctors, we use personal NSC projects ofGerard Jennhwa Chang to hire post doctorsjoining the program. They are Changhong Lu,J. Qian, Fei-Huang Chang, Yongqiang Zhao,Jiaojiao Wu.Since 2004, the discrete mathematics groupin south has invited 13 visitors from abroad.The financial support of our group is limited(with NT$300,000 per year, which includessupport for visitors and local activities), we areunable to support long term visitors. The staysof our visitors are from one week to onemonth. However, we made efforts to makeshort time visits fruitful. Instead of havingshort time visitors come-talk-leave, we try toinitiate collaboration before visitors start theirvisits. Select visitors who share commoninterests with member of local group, andprepare ourselves and students for comingvisitors, and make the best use of visitor's timeduring their stay in Taiwan. There are manyjoint papers of members of the group and ourvisitors are finished or under preparation,resulting from their visits to our group. Somevisits initiated long term collaborations. A visitof Professor Andre Raspaud from BordeauxFrance initiated a two year collaborationproject supported by NSC and CNRS, and ajoint supervising program between NSYSUand Bordeaux University.Each semester, the discrete mathematicsgroup in north and south has series ofseminars. Some of the seminar talks are givenby visitors and some talks from groupmembers, post doctors and students.The discrete mathematics group organizedfour local workshops and two internationalconferences. Speakers of the workshops arefrom Taiwan. Each workshop focuses onproblems in a special topic. Our purposes areto get students involved in our program andalso enhance collaborations among localresearchers. The two conferences aim tobridge local researches with experts aboard.One Conference has 49 speakers and the other61 speakers.As NCTS aims to train talented studentsand promote young researchers, we design thestudent summer research program for studentswho have strong interest in mathematicsresearch. In 2005, we have the topic "GraphColoring and Related Topics" (2005.7.11-2005.8.19) with 9 selected students. There is a13 ‹‹- Highlights of the Programs

egular lecture from 9:00 to 11:00 every weekday. Problems for discussion are assignedduring the lectures, and the posted on the web.From 11:00 to 14:00, students have free timeto do the assigned problems by themselves.There is then a discussion time for all studentsand the lecturer from 14:00 to 16:00. Someproblems may be solved at the same day theyassigned, but some may be solved the otherdays. During this period, totally about 100problems are assigned, some of them aretypical exercises while some are researchproblems. Among them, about 70% are solvedcompletely by the students and some aresolved partially. As the organizer needs toattain the Pacific Rim Conference, XudingZhu chipped in for the rest of the program. In,2006 we have "Graph Ramsey Theory"(2006.7.10-2006.8.18) with 5 selectedstudents. The running method is the same asthe previous one. During this period, totallyabout 70 problems are assigned, some of themare typical exercises while some are researchproblems. Among them, about 70% are solvedcompletely by the students and some aresolved partially.As the probabilistic method becomes moreand more important in the study of discretemathematics, we invited Professor Hong-GwaYeh (NCU) offering a regular course"Probabilistic Method" on Tuesday morningsfrom September 2006 to January 2007. Tomake it formal, we do cooperate with theDepartment of Mathematics of NationalTaiwan University to make it as a regularcourse offering credits to students attaining theclasses. Professor Yeh's lecture is based on thebook "Probabilistic Method" by Alon andSpencer, plus many personal notes andmaterials posted on his web page. Besides thestudents and I, we also have faculties ofAcademia Sinca and probability people of mydepartment attaining the classes.Local Focus GroupNorth: Gerard Jennhwa Chang (NTU), Ko-WeiLih (AS), Jing-Ho Yan (Aletheia),Hsun-Wen Chang (Tatung), Chiang Lin(NCU), Hong-Gwa Yeh (NCU), Sheng-Chyang Liaw (NCU), Roger Kwan-Ching Yeh (Feng-Chia), David Kuo(NDHU), post doctors and graduatedstudents.South: Xuding Zhu (NSYSU), Meng-Na Lo(NSYSU), Tsai-Lien Wong (NSYSU),Li-Da Tong (NSYSU), Mei-Hui Guo(NSYSU), Zhishi Pan (NSYSU), Sen-Peng Eu (NUK), Szu-En Cheng(NUK), Hong-Gwa Yeh (NCU), plus 5Ph.D. students.Visitors• Wen-Ling Huang, University of Hamburg,(2004.9.19-2009.10.17),• Yuan Hong, East Chia Normal University,(2004.9.29-2004.10.4),• Jerrold R. Griggs, University of SouthCarolina (2005.5.22-2005.5.24),• Jae-Hoon Kwon, University of Seoul,(2006.8.6-2006.8.19),• Khee Meng Koh, National University ofSingapore, (2007.6.16-2007.6.29),• Frank Kwang-Ming Hwang, (2007.6.21-2007.6.30),• Sandi Klavzar, University of Maribor,Slovenia, (2004.9.22-2004.10.1),• Zhidong Bai, National Singapore University,Singapore, (2004.9.19-204.9.23),• Daniel Kral, Charles Unviersity, CzechRepublic, (2004.12.5-2004.12.21),• Andre Raspaud, Universite Bordeaux,France, (2005.1.8-2005.1.28),• Pavol Hell, Simon Fraser Univerity, Canada,(2005.12.8-205.12.13),• Mike Albertson, Smith college, USA,(2005.12.9-2005.12.13),• Claude Tardif, Royal Military College,Canada, (2005.12.19-2005.12.28),• Douglas West, University of Illinois atUrbana-Champaign, USA, (2005.12.19-2005.12.23),• Daqing Yang, Fuzhou University, PRC,(2006.1.19-2006.2.19 and 2007.6.30-2007.7.22),• Wensong Lin, South-East University,Nanjing, PRC, (2006.1.20-2006.2.20,2007.6.30-2007.7.22),Highlights of the Programs -›› 14

• Alexandr Kostochka, University of Illinois atUrbana-Champaign, USA, (2007.1.5-2007.1.15),• Serguei Norine, Georgia Institute ofTechnology, USA, (2007.3.5-2007.3.15),• Peter Horak, University of Washington,Tacoma, USA, (2007.3.12-2007.3.25).Workshops and Conferences• Workshop on Graph Coloring, (2004.7.24-7.26). Speakers: X. Zhu, G. Chang, B. Chen,H. Yeh.• CTS Conference on Combinatorics and ItsApplications, in Honor of Frank K. Hwang's65 th Birthday, (2005.5.19-2005.5.21). InvitedSpeakers: G. J. Chang, C.-S. Chang, C. J.Colboum, D.-Z. Du, G. Fan, J. R. Groggs, C.Rodgers, U. Rothblum, J. H. Spencer, R. M.Wilson. There are 39 contribution talks.• Workshop on Edge Coloring and GraphDecomposition, (2005.8.5-2005.8.6).Speakers: H. Fu, C. Fu, W. Hu, K. Huang, Q.Lin, S. Wu.• Workshop on Quantum Algorithms,(2005.8.23). Speakers: D. Guan, Y. Wong, S.Zhuan.• Workshop on Graph Theory and Network,(2007.6.20). Speakers: W. Wang, Y. Bu, L.Xiong, S. Zhou.• 2007 International Conference on GraphTheory and Combinatorics & Fourth CorssstraitConference on Graph Theory andCombinatorics. (2007.6.24-2007.6.29).Plenary speakers: G. Fan, F. K. Hwang, Y.-N. Yeh, X. Yu, X. Zhu. There are 56contribution talks.International CooperationInitiated during Professor Andre Raspaud'svisit in 2005, which was supported by NCTS,the focus group started a 2 year joint projectwith LaBRI, Universite de Bordeaux I,supported by NSC and CNRS. Under the jointproject, X. Zhu and a graduate student visitedUniversite de Bordeaux, and A. Raspaud andA. Pecher visited National Sun Yat-senUniversity. L. Tong is planning a visit toBordeaux in August, 2007.Part II: The AccomplishmentIn the north, selected publications are listedbelow with their descriptions follow.[175] F.-H. Chang, G. J. Chang and C. Lu,Distance-two labelings of graphs,preparing.[174] G. J. Chang and C. Lu, Full Color ofgraphs with small numbers of edges,preparing.[145] Y.-Y. Chien and G. J. Chang, The upperdomination of Cartesian products ofgraphs, preparing.[168] J.-J. Chen and G. J. Chang, Distancegraphs on R n with 1-norm, J. Combin.Optimization (accepted).[161] R.-Y. Wu, G.-H. Chen, Y.-L. Kuo andG. J. Chang, Node-disjoint paths onhierarchical hypercube networks,Inform. Sciences (accepted).[151] B.-J. Li and G. J. Chang, Cliquecoverings and partitions of line graphs,Discrete Math. (accepted).[137] J. S.-T. Juan and G. J. Chang, Adaptivegroup testing for consecutive positives,Discrete Math. (accepted).[135] Y.-P. Tsao and G. J. Chang, Profileminimization of compositions ofgraphs, J. Combin. Optimization(accepted).[129] J. S.-T. Juan and G. J. Chang, Grouptesting in graphs, J. Combin.Optimization (accepted).[169] G. J. Chang, S.-P. Eu and C.-H. Yeh, Onthe (n,t)-antipodal Gray codes, Theore.Comput. Sci. 374 (2007) 82-90.[162] G.-Y. Chang, G.-H. Chen and G. J.Chang, (t,k)-Diagnosis for matchingcomposition networks under MM*model, IEEE Trans. Computers 56(2007) 73-79.[146] J.-J. Pan and G. J. Chang, Induced-pathpartition on graphs with special blocks,Theore. Comput. Sci. 370 (2007) 121-130.[144] C.-C. Lin, G. J. Chang and G.-H. Chen,15 ‹‹- Highlights of the Programs

Locally connected spanning trees ofproper circular-arc graphs, DiscreteMath. 307 (2007) 208-215.[131] G. J. Chang, C. Lu, and S. Zhou, Nohole2-distance colorings for Cayleygraphs on finitely generated abeliangroups, Discrete Math. 307 (2007)1808-1817.[119] G. J. Chang, J.-J. Chen, D. Kuo, and S.-C. Liaw, Distance-two labelings ofdigraphs, Discrete Applied Math. 155(2007) 1007-1013.[157] G. Y. Chang, G. H. Chen and G. J.Chang, (t,k)-Diagnosis for matchingcomposition networks, IEEE Trans.Computers 55 (2006) 88-92.[150] M. Zhao, L. Kang and G. J. Chang,Power domination in graphs, DiscreteMath. 306 (2006) 1812-1816.[148] Y.-P. Tsao and G. J. Chang, Profileminimization on product of graphs,Discrete Math. 306 (2006) 792-800.[139] J.-J. Pan and G. J. Chang, Isometricpathnumbers of graphs, Discrete Math.306 (2006) 2091-2096.[175] In the study of the distance-twolabeling problem, graphs G with distance-twolabeling number (G) = 2 (G) and hallnumber (G) = (G) play a critical role,where (G) is the maximum degree of G.Previous results show that many such kind ofgraphs have numbers of vertices polynomial in(G). People believe that the desiredproperties should constrain the graphs in somespecial shapes and so the numbers of verticescan only be polynomial in terms of (G). Ourrecent study show that there are much morefreedom on these kind of graphs. In particularsuch kind of graphs with numbers of verticesexponential in (G) are plentiful, please see[175] in the publication list.[145] The well known conjecture proposedby Vizing for the domination problem statesthat (G H) ≥ (G) (H) for any graphsG and H, where (G) and (H) are thedomination numbers of G and H respectively.A related conjecture proposed by Nowakowskiand Rall states that (G H) ≥ (G) (H),where (G) and (H) are the upperdomination numbers of G and H respectively.Clark and Suen recently establish a strongerresult that (G H) ≥ (G) (H) + 1 forany graphs G and H. They then ask for astronger bound that (G H) ≥ (G) (H)+ min{|V(G)| (G), |V(H)| (H)} for anygraphs G and H. We have just settled thisquestion, please see [145] in the publicationlist.[174] It is proved that a graph G = (V, E)with |V| 1 |E| |V| is full colorable exceptwhen G is one of some particular graphs,where the graph G is called full colorable if ithas a no-hole (G)-L(2,1)-labeling.[168] Degrees of vertices, connectivity andchromatic numbers of various distance graphsin the n-dimensional spaces using 1-norm andthe subsets of all lattice points of the n-spacesare obtained.[161] The concept of wide-diameter,introduced by Frank Hsu, unifies connectivityand diameter. This paper gives node-disjointpaths for hierarchical hypercube networksbetter than previous constructions.[151] A unified and simple proof forprevious results on clique coverings and cliquepartitions is given. Using the same prooftechnique, we also give a simple proof for theDe Bruijn-Erdos Theorem[137] Combinatorial group testing has wideapplications in the real world. In this paper, wegive bounds on the adaptive group testing forconsecutive positives which is better thanprevious constructions.[135] Profile numbers for graphs obtainedfrom various operations are determined, wherethe graph operations include Cartesianproduct, join, composition, tenser product andstrong product …etc.[131] The study of colorings withconditions at distance two arise from thechannel assignment problem. In this paper, wegive no-hole 2-distnace colorings of someCayley graphs by using a group-theoreticapproach.Highlights of the Programs -›› 16

[129] The bipartite graph conjecture forgroup testing says that every bipartite graph of2 n edges always has an induced sub-graph ofthe half number of edges. Toward to the studyof the conjecture, we give a bound for theoptimal numbers of testing that is better thanprevious ones.As for the south, activities organized by thefocus group and exchange of visits havestimulated collaborations between local groupmembers and visitors from abroad. There are13 joint papers that are closely related to thevisits to the group, either initiated during theirvisits or initiated before the visits and madeprogress during the visits. Selectedpublications of the local group since 2004:[1] T. Kaiser, D. Kral, R. Skrekovski, X. Zhu,The circular chromatic index of graphs ofhigh girth, Journal of CombinatorialTheory Series B, 97 (2007) 1-13.[2] S. Eu, T. Fu, The Cyclic SievingPhenomenon for Faces of GeneralizedCluster Complexes, Advances in AppliedMathematics, accepted.[3] S. Eu, T. Fu, Y. Yeh, Refined Chung-FellerTheorem, Journal of Combinatorics Theoryseries A, accepted.[4] S. Eu, S. Liu, Y. Yeh, On the Congruencesof Some Combinatorial Numbers, Studiesin Applied Mathematics, 116 (2006), 135-144.[5] P. Afshani, M. Ghandehari, M. Ghandehari,H. Hatami, R. Tusserkani, X. Zhu, Circularchromatic index of graphs of maximumdegree 3, Journal of Graph Theory, 49(2005), 325-335.[6] S. Klavzar, T. Wong, X. Zhu,Distinguishing group actions on vectorspaces and graphs, Journal of Algebra, 303(2006), 626-641.[7] S. Klavzar, X. Zhu, Cartesian powers ofgraphs can be distinguished by two labels,European Journal of Combinatorics,accepted.[8] Z. Pan, X. Zhu, Minimal circular-imperfectgraphs of large clique number and largeindependence number, European Journal ofCombinatorics, accepted.[9] D. West, X. Zhu, Circular chromatic indexof product of graphs, Journal of GraphTheory, accepted.[10] A. Raspaud, X. Zhu, List circular coloringof trees and cycles, Journal of GraphTheory, accepted.[11] A. Pecher, X. Zhu, On the circularchromatic number of circular partitionablegraphs, Journal of Graph Theory,accepted.[12] D, Kral, L. Tong, X. Zhu, UpperHamiltonian number and Hamiltonianspectra of graphs, Australasian Journal ofCombiantorics, 35 (2006), 329-340.[13] G. J. Chang, S. Eu, C. Yeh, On theantipodal Gray codes, TheoreticalComputer Science, 374 (2007), 82-90.A. Graph coloring. Graph coloring is acentral topic in graph theory. Circular coloringof graphs is a concept that are most studied inthis group. The circular chromatic index ofgraphs (i.e., the circular chromatic number ofline graphs) is a difficult topic, with manyopen problems and few results. A surprisingresult is obtained in [5], where it is proved thatthe circular chromatic index of a graph ofmaximum degree at most 3 is either 4, orbounded by 11/3. In particular, it is shown that2-edge connected cubic graphs have circularchromatic index at most 11/3. This resultstimulated further research in this direction.Kaiser, Kral and Skrekovski showed that cubicgraphs of large girth have circular chromaticnumber close to 3. This result is greatlyimproved in [1], where it is proved that graphswith maximum degree k and large girth hascircular chromatic index close to k. West andZhu [9] investigated the circular chromaticindex of the Cartesian product of graphs anddetermined the value of χ' c (C 2k+1 C 2m+1 )form≥3k+1. Another fast developing areaconcerning circular coloring of graphs is thecircular choosability of graphs. The joint workof Raspaud and Zhu [10] gives a completecharacterization of color-size list assignmentsl for which a tree is circular l -choosable.Tight bounds for cycles are obtained there.17 ‹‹- Highlights of the Programs

Before and during the visits of Serguei Norinefrom Georgia Institute of Technology, T. Wongand X. Zhu have worked together with him tosuccessfully apply algebraic methods to solveproblems concerning circular choosability. Afew joint papers (by W. Lin, C. Yang, D. Yang,X. Zhu, S. Norine, Z. Pan) on consecutivecircular choosabilities of graphs are initiatedduring our visitors' stay in Taiwan, and areeither submitted or under revision.B. Cluster combinatorics. The notion ofcyclic sieving phenomenon was introduced byReiner, Stanton, and White as a generalizationof Stembridge's q = 1 phenomenon. Thegeneralized cluster complexes associated toroot systems are given by Fomin and Readingas a generalization of the cluster complexesfound by Fomin and Zelevinsky. S. Eu and T.Fu have shown that the faces of variousdimensions of the generalized clustercomplexes in type An, Bn, Dn, and I 2 (a) areshown to exhibit the cyclic sievingphenomenon under a cyclic group action. Forthe cluster complexes of exceptional type E 6 ,E 7 , E 8 , F 4 , H 3 , and H 4 , a verification for such aphenomenon on the facets is given.C. Enumerative Combinatorics. Variousproblems and applications on EnumerativeCombinatorics, centered on lattice paths andtree structures, are considered. Including thecharacterization of the (n, t) antipodal Graycodes when n is odd, the area counting underDyck paths on the check board and its relationwith pattern-avoid permutations, thecomputing of the generalized Wiener index,the new simple proof of the Aztec diamondtheorem, the enumeration of the k-leadingfunctions for generalized parking functions,and a refinement for classic Chung-Fellertheorem and a characterization for the Chung-Feller type theorem.D. Distinguishing labeling of graphs andgroup actions. This is a research topic thatwas initiated during S. Klavzar's visit to ourgroup, and have been fruitfully carried outlater on. The question started with findinglabeling of a graph with minimumlabels sothat identity is the only automorphism of thegraph which preserves the labels. Theminimum number of labels used in such alabeling is called the distinguishing number ofthe graph. To answer this question, it isimportant to understand the structure of theautomorphism group of the graph. Onespecific question studied first by Albertson andCollins is this: what are the possible values ofthe distinguishing number of a graph withautomorphism group isomorphic to thesymmetric group Sn? This question is nowcompletely solved (in a paper byT.Wong and X. Zhu under revision).Moreover, a complete answer is also given tothe question as what are the possible values ofthe distinguishing number of actions of Sn andAn.Highlights of the Programs -›› 18

D.3 Dynamical Systems at NCTS 2004-2007Coordinator: Song-Sun Lin (National Chiao Tung University)Part I: Background and Activities inthe Programynamical System is one of the majorand classical research areas inmathematical science. In the sequence ofdynamical systems programs, we emphasizethe theory and the applications of dynamicalsystems. We also cooperate with the people inthe topical program of scientific computationto study the computation of chaotic dynamicalsystems.During the period, we also organize astudent's seminar so that the graduates can bewell trained. The activities and visitingscholars are listed in the following.Local Focus GroupS.-S. Lin (NCTS Center Scientist andNCTU), J. Juang (NCTU), C.-W. Shih(NCTU), M.-C. Li (NCTU), K.-C. Chen(NTHU)Post DoctorsC.-T. Wu (NCTS 2004-05), T.-H. Yang(NCTS 2003-04), J.-C. Ban (NCTS 2003-06)Frequent ParticipantsB.-S. Du (Academia Sinica), Y.-C. Chen(Academia Sinica), K.J. Palmer (NTU), T.-Y.Yang (Tamkang Univ.), C.-H. Hsu (NCU), S.-B. Hsu (NTHU), W.-W. Lin (NTHU), C.-J. Yu(NCTU), T.-S. Yang (Tung-Hai Univ.), C.-N.Chen (NCUE), C.-Y. Cheng (NPUE), J.-C.Ban (NHLUE)Long Term Visiting ScientistGoong Chen (Texas A&M University),2006 Fall, at NTHUShort Term VisitorsZin Arai (Kyoto Univ.), Yong Moo Chung(Hiroshima Univ.), Jin Hatomoto (TokyoMetropolitan Univ.), Shin Kiriki (KyotoUniversity of Education), Hiroshi Kokubu(Kyoto Univ.), Masashi Kisaka (Kyoto Univ.),Eiko Kin (Kyoto Univ.), Toshikazu Ito(Ryukoku Univ.), Hiroe Oka (Ryukoku Univ.),Toshiyuki Ogawa (Osaka Univ.), MitsuhiroShishikura (Kyoto Univ.), Naoya Sumi (TokyoInstitute of Technology), Masato Tsujii(Hokkaido Univ.), Valentin Afraimovich(Investigator of San Luis Potosi University,Mexico), Anatoli Babin (UC Irvine ), KeningLu (Brigham Young University), Alica Miller(University of California, Irvine), RogerNussbaum ( Rutgers University ), MarceloViana (IMPA Rio de Janeiro), Xiangdong Ye(USTC), James Yorke (University ofMaryland), Leon Glass (McGill University),Henk Broer (University of Groningen), WalterCraig (McMaster University), Luigi Chierchia(Univerità Roma 3 ), Rafael Ortega(Universidad de Granada), Zhihong Jeff Xia(Northwestern University), Luca Dieci(Georgia Tech), Russell Johnson (Università diFirenze ), Peter Kloeden (Johann WolfgangGoethe University), Weishi Liu (University ofKansas), Mason Porter (Georgia Institute ofTechnology), Hildebrando Munhoz Rodrigues(Universidade de São Paulo), Huiping Zhu(York University), Yingfei Yi (GeorgiaInstitute of Technology), Rick Moeckel(University of Minnesota), Eusebius Doedel(Concordia University), Piotr Zgliczynski(Jagiellonian University), Hal Smith (ArizonaState University), Jinqiao Duan (IllinoisInstitute of Technology), Xiao-Qiang Zhao(Memorial University of Newfoundland),Gareth Roberts (College of the Holy Cross),Pawel Pilarczyk (Kyoto University)19 ‹‹- Highlights of the Programs

Special Courses in 2004-2007• Theory and Applications of DynamicalSystem (IV), 2007 spring.• Speaker : S.-S. Lin (NCTU)• Theory and Applications of DynamicalSystem (III), 2006 fall.• Speaker : S.-S. Lin (NCTU)• Theory and Applications of DynamicalSystem (II), 2006 spring.• Speaker : S.-S. Lin (NCTU)• Theory and Applications of DynamicalSystem (I), 2005 fall.• Speaker : S.-S. Lin (NCTU)Conferences and Workshops• 2007 CTS Workshop on Dynamical Systems,May 14-18,• 2007 at NCTS. Organizers : K.-C. Chen(NTHU), J. Juang (NCTU), M.-C. Li(NCTU) and C.-W. Shih (NCTU).• International Conference on Chaos andDynamical Complexity, May 24-30, 2006 atNCTS. Organizers : S.-N. Chow (GeorgiaInst. Of Tech.), S.-S. Lin (NCTU).• International Conference on Chaos andDynamical Complexity, May 16-20, 2005 atNCTS. Organizers : S.-N. Chow (GeorgiaInst. Of Tech.), S.-S. Lin (NCTU), W.-W.Lin (NTHU), Y.-F. Yi (Georgia Inst. OfTech.).• Japan-Taiwan Conference on DynamicalSystems, March 21-26, 2005 at NCTS.Organizer: S.-S. Lin (NCTU), C.-W. Shih(NCTU), Hiroshi Kokubu (Kyoto Univ.).• NCTS 2004 International Conference onDynamical Systems, June 23-28, 2004 atNCTS. Organizer: S.-S. Lin (NCTU), Y.-F.Yi (Georgia Inst. Of Tech.), C.-N. Chen(NCUE), Kenning Lu (MSU), Jiangong You(NJU)Student's Seminars and Schools• NCTS 2007 Summer Course on DynamicalSystems• NCTS 2006 Summer Program ---JointProgram of Dynamical Systems andMathematics Biology• NCTS Joint Seminar in Math. Biology &Dynamical Systems 2006• Monotone Dynamical Systems and ItsApplication to Population Biology 2006• This intensive course will basicallyfollows the book "Monotone DynamicalSystems" of Hal Smith (1995) and his recentsurvey paper with Hirsch "MonotoneDynamical Systems" (2004). We shall firstintroduce the ODE of cooperative systems asthe first example of Monotone Flow. Thenwe present the monotone flow in abstractspace and its basic properties. Theapplication of the theory to 3-dimensioncompetitive system and several biologicalmodels will be discussed. Then we apply thetheory to reaction-diffusion equations , delaydifferential equations and maps.• Topical Program in Dynamical Systems 2006Fall• We will begin with many concrete modelsof ODEs and PDEs in dynamical systemtheory and quantum mechanics. From thegiven models, we examine their invarianttransformations, Lie groups and invariants.Using invariants corresponding to the Liealgebra structure, we seek ways to reduce theODEs and PDEs to lower order systems andsometimes even Explicit solutions of thephysical model, and the physicalimplications.• This course utilizes only basic knowledgein ODEs, PDEs and algebra. Students do notneed extensive prerequisites in thesesubjects.• NCTS Student Seminar on DynamicalSystems 2007Part II: The Accomplished and theAnticipations[1] K.-C. Chen, Existence and MinimizingProperties of Retrograde Orbits to theThree-Body Problem with Various Choicesof Masses. Annals of Math., to appear.[2] S.-S. Lin, Patterns generation and spatialentropy in two-dimensional lattice models,to appear in Asian Journal of MathematicsHighlights of the Programs -›› 20

(with J.-C. Ban and Y. H. Lin).[3] C.-W. Shih, Multistability and convergencein delayed neural networks, Physica D, toappear (with C.-Y. Cheng and K.-H. Lin).[4] M.-C. Li, Chaotic dynamics in anoverlapping generations model withmyopic and adaptive expectations, Journalof Economic Behavior and Organization, toappear (with H.-J. Chen and Y.-J. Lin).[5] J. Juang, Global synchronization in latticesof coupled chaotic systems, Chaos, toappear (with C.-L. Li and Y. H. Liang).[6] S.-S. Lin, Smooth solutions to a class ofquasilinear wave equations, J. DifferentialEquations, 224, 229-257, 2006 (with C.-H.Hsu and Tetu Makino).[7] K.-C. Chen, Removing CollisionSingularities from Action Minimizers forthe N-body problem with Free Boundaries.Arch. Rational Mech. Anal. 181, 311-331,2006.[8] M.-C. Li, Topological horseshoes forperturbations of singular differenceequations, Nonlinearity, 19, 795-811, 2006(with M. Malkin).[9] M.-C. Li, Topological horseshoes forArneodo-Coullet-Tresser maps, Regularand Chaotic Dynamics, 11, 181-190, 2006(with B.-S. Du and M. Malkin).[10] J. Juang, Eigen curve problems andapplication to the wavelet method ofchaotic control, J. Math. Phys., 47 122702, 2006 (with C.-L. Li).[11] J. Juang, Eigen value problems andapplication to the wavelet method ofchaotic control, J. Math. Phys., 47072704, 2006 (with C.-L. Li).[12] C.-W. Shih, Multistability in recurrentneural networks, SIAM J. AppliedMathematics, Vol.66, No. 4, 1301-1320,2006 (with C.-Y. Cheng and K.-H. Lin).[13] C.-W. Shih, Transition to intermittentchaotic synchronization, Phys. Rev. E 72,036212, 2005 (with Liang Zhao and Y.-C.Lai).[14] S.-S. Lin, Patterns generation andtransition matrices in multi-dimensionallattice models, Discrete and ContinuousDynamical Systems, Vol. 13, 637-658,2005 (with J.-C. Ban).[15] M.-C. Li, Qualitative property betweenflows and numerical methods, NonlinearAnalysis, 59, 771-787, 2004.[16] S.-S. Lin, On spherically symmetricsolution of the relativistic Euler equation,J. Differential Equations, Vol. 201, 1-24,2004 (with C.-H. Hsu and Tetu Makino).21 ‹‹- Highlights of the Programs

D.4 Geometric Analysis at NCTS 2004-2007Coordinator: Shu-Cheng Chang (National Tsing Hua University) and Dong-Ho Tsai (National Tsing Hua University)Part I: Background and Activities inthe Programhe field of Geometric Analysis (GA)has seen spectacular growth anddevelopment in the past twenty years.Analytic, geometric and topologicaltechniques are used in the setting ofdifferential geometry to solve problems inglobal geometry and topology, mathematicalphysics, algebraic geometry, materials science,image processing and optimization. A plethoraof important geometric heat flows are ofcurrent interest, including Ricci and Kaehler-Ricci flow, mean and inverse mean curvatureflows, Yamabe flow, harmonic map flow,Gauss curvature flow, flows of hypersurfacesby symmetric functions of principalcurvatures, Yang-Mills heat flow, flows ofcurves and submanifolds, and heat flows incontact geometry. These flows arecharacterized by the deformation of geometricobjects or structures such as metrics,connections, mappings, submanifolds, andforms by geometric quantities such ascurvature and consist of partial differentialequations of parabolic type. Via geometricevolution equations, the powerful methods ofnonlinear analysis can be applied tomathematical problems which can beapproached geometrically. Another importantsubject in geometric analysis is sub-ellipticpartial differential equations and sub-Riemannian geometry which has veryimportant applications in several complexvariables and even biomedical sciences.GA at NCTS is considered as a broad field.One can view it as a combination ofDifferential Geometry and Partial DifferentialEquations. Roughly speaking, the main themeis to use analytical methods (function andoperator theory, comparison method, a prioriestimate of partial differential equation,Hamiltonian mechanics, etc.) to studyproblems related to geometry. Furthermore,one may to construct fundamental solution forPartial Differential Equation in terms ofgeometric invariants.GA is one of the emphasizing researchprogram supported by NCTS. Activities atNCTS related to GA include seminars (withtalks given by local or foreign visitors ofNCTS), mini-courses, international workshopsand conferences. These activities are run bylocal and/or foreign visitors.Local VisitorsBy local visitors we mean mathematiciansresiding in Taiwan. During the years of 2004-2007, the following people have participatedin GA program or activities at NCTS:T.-P. Liu, J.-H.Cheng, S.-J. Kan, K.-M.Hui,C.-C. Hsieh, Derchi Wu (Academia Sinica),C.-C. Chen, Y.-I. Lee, T.-C. Lin, C.-S. Lin(NTU), J.-S. Guo, C.-C. Lin, (NTNU), M.-R.Li, L.-Y. Tsai (NCU), F.-C. Liu, C.-T. Shieh(Tamkang University), J.-L. Chern, C.-L.Wang, H.-W. Lin, M.-L. Yau (NCU), H.-L.Chiu (Chung Yuan Christian University), S.-C.Chang, D.-H. Tsai, R.-T. Chen (NTHU), M.-K.Chuah, C.-K. Lin (NCTU), C.-N. Chen(NCUE), C.-J. Sung, S.-C. Chu, S.-Y. Hsu(NCCU), Y.-J. Hung, Roger Chen, Eugene Xia(NCKU), C.-T. Wu, Hsungrow Chan (NPUE),J.-C. Tsai (NTOU)There are also several Ph.D. studentsconstantly involved in the GA activities atNCTS. They are from universities includingNTU, NTHU and NCCU.Foreign Short-term VisitorsThese foreign short-term visitors of NCTSusually stay in Taiwan for several days or upto at most two weeks. They were mostlyHighlights of the Programs -›› 22

invited by mathematicians of Taiwan, with thehope of increasing future researchcollaboration and cultivating workingrelationships. The list of foreign short-termvisitors for the years of 2004-2007 consists ofthe following. It does not include visitors ofNCTS who just come to Taiwan for attendingan international conference.Richard Beals (Yale University), AliceSun-Yung Chang (Princeton University),Jianguo Cao (University of Notre Dame), Der-Chen Chang (Georgetown University), XinfuChen (University of Pittsburgh), BennettChow (UC-San Diego), Yenheng Ding(Academia Sinica, Beijing), Wayne Eby(Temple University), Kenro Furutani (TokyoUniversity of Sciences), Bernard Gaveau(University of Paris 6), Peter Greiner(University of Toronto), Eric Grinberg(University of New Hampshire), Wen-LingHuang (University of Hamburg), Qing Han(University of Notre Dame), Chisato Iwasaki(University of Hyogo), Sergei Kuznetsov(University of Colorado), Bao Qin Li (FloridaInternational University), Conan Leung(University of Minnesota), Peng Lu(University of Oregon), Irina Markina (BergenUniversity) , Ngaiming Mok (University ofHong Kong), Richard Palais (UC-Irvine),Peter Polacik (University of Minnesota), Yum-Tong Siu (Harvard University), Chuu-LianTerng (UC-Irvine), Jingzhi Tie (University ofGeorgia), Alexander Vasiliev (BergenUniversity), Guofang Wang (Max PlanckInstitute), Paul Yang (Princeton University),Yisong Yang (Polytechnic University),Horng-Tzer Yau (Harvard University), Shing-TungYau (Harvard University)Foreign Long-term VisitorsThese foreign long-term visitors of NCTSusually stay in Taiwan for more than twoweeks and give a series of survey lectures ormini-courses. The list of foreign long-termvisitors for the years of 2004-2007 consists ofthe following. Their topics of talks are alsoincluded.• Xi-Ping Zhu, Zhongshan University, China,2004. Topic: Ricci Flow on RiemannianManifold.• Bing-Long Chen, Zhongshan University,China, 2004. Topic: Kaehler-Ricci Flow andRelated Topics.• P. T. Chrusciel, Universite de Tours, France,2004. Topic: Mathematical Aspects ofGeneral Relativity.• J. Isenberg, University of Oregon, USA,2004. Topic: Mathematical Aspects ofGeneral Relativity.• Tai-Peng Tsai, University of British-Columbia, Canada, 2004. Topic: Mini-Course on Bose-Einstein Condensation.• Tai-Peng Tsai, University of British-Columbia, Canada, 2005. Topic: NonlinearPDE and Particle System.• Tai-Peng Tsai, University of British-Columbia, Canada, 2006. Topic: RegularityProblem for the Navier-Stokes Equations.• Guofang Wang, Max Planck Institute,Germany, 2004. Topic: Toda System andLiouville Type Equations.• Jiaping Wang, University of Minnesota,USA, 2005. Topic: Topics in GeometricAnalysis.• Mu-Tao Wang, Columbia University, USA,2005. Topic: Introduction to Mean CurvatureFlow Equations.• Jianguo Cao, University of Notre Dame,USA, 2005-2006. Topic: Lecture on GromovCompactness Theorem.• Bang-Yen Chen, Michigan State University,USA, 2006. Topic: Topics in Submanifolds.• Der-Chen Chang, Georgetown University,USA, 2006, 2007. Topic: Sub-elliptic PartialDifferential Equations and sub-RiemannianGeometry.• Ovidiu Calin, Eastern Michigan University,USA, 2006. Topic: Analysis: GeometricMechanics on sub-Riemannian Manifolds.Post Doctors• Marcello Lucia, 2004-2005.• C.-T. Wu, 2004-2005.Mini-coursesFor the years of 2004-2007, NCTS hassponsored the following mini-courses run bylocal and foreign scholars:23 ‹‹- Highlights of the Programs

• Symmetry Method and Their Applications,September, 2004 - January, 2005.• Advanced Course on Geometric Analysis,September 19 - December 26, 2005.• A priori Estimate for Partial DifferentialEquations of Elliptic Type and RelatedTopics, summer, 2005.• Summer Course on PDE in MathematicalPhysics, Summer, 2006.• Topical Program in Analysis andGeometry, Spring, January-July, 2007.Workshops and ConferencesFor the years of 2004-2007, NCTS hasorganized the following GA relatedinternational workshops and conferences:• International Conference on Elliptic andParabolic Problems: Recent Advances.February 16-20, 2004. 25 speakers fromforeign countries, 5 speakers from Taiwan.• Workshop on Reaction-Diffusion Equationsand Related Topics. May 26-31, 2004. 16speakers from foreign countries, 8 speakersfrom Taiwan.• Workshop on Differential Geometry. October20-22, 2004. 16 speakers from foreigncountries, 8 speakers from Taiwan.• Mini-course and Workshop on ConformalInvariant-Analytic and Geometric Aspects.June 6-14, 2005. 13 speakers from foreigncountries.• France-Taiwan Joint Conference onNonlinear Partial Differential Equations andRelated Topics. July 18-22, 2005. 15speakers from foreign countries, 10 speakersfrom Taiwan.• Recent Development of Mathematics atTsing Hua University. June 6, 2006. 3speakers from Tsing Hua University, 1speakers from USA.• Latest Development of Geometric Analysis.June 8-9, 2006. 8 speakers from Taiwan.• Taiwan-AMS Joint International Conference.December 14-18, 2005. 20 speakers fromforeign countries, 8 speakers from Taiwan.• Workshop on Geometry and NonlinearAnalysis. December 20-21, 2005. 4 speakersfrom foreign countries, 3 speakers fromTaiwan.• NCTS Workshop on Geometry and Analysis.January 8-9, 2006.• Workshop on Reaction-Diffusion Equations:Theory and Applications. December 1-2,2006. 6 speakers from foreign countries, 6speakers from Taiwan.• International Conference on NonlinearAnalysis. November 20-25, 2006. 30speakers from foreign countries, 10 speakersfrom Taiwan.• International Conference on GeometricAnalysis. January 16-18, 2007. The speakerswere Alexander Vasiliev and Irina Markinafrom Norway; Bernard Gaveau from France;Peter Greiner from Canada; Chisato Iwasakiand Kenro Furutani from Japan; Der-ChenChang and Jingzhi Tie from USA; Hung-Ling Chiu and Shu-Cheng Chang fromTaiwan. All speakers gave nice talks ondifferent topics in sub-elliptic partialdifferential equations and sub-Riemanniangeometry, analysis on CR manifolds, pseudodifferentialoperator and its applications tocomplex analysis.• Workshop in Analysis and Geometry. March5-6, 2007. This workshop was supportedjointly by NCTS and the Academia Sinica.The speakers were Bernard Gaveau fromFrance; Peter Greiner from Canada; RichardBeals, Der-Chen Chang and Jingzhi Tie fromUAS; De-Chi Wu and Chun-Chung Hsiehfrom Taiwan.• International Conference on GeometricAnalysis. June 18-22, 2007. This was a biginternational conference which wassupported by NCTS and Taida Institute ofMathematical Sciences. Speakers includedPeter Li, D.H. Phong, H.D. Cao, JianguoCao, Der-Chen Chang, Ahanyu Ji, JohnLoftin, Lei Ni Jon Wolfson, Mu-Tao Wang,Jiaping Wang, Stephen S.T. Yau from USA;Ben Andrews from Australia; G. Huiskenfrom Deutschland; B. Wilking fromGermany; Sumio Yamada from Japan; L.-F.Tam, Nai Chung Leung from Hong Kongand Shu-Cheng Chang, Yng-Ing Lee, Jih-Hsin Cheng, J.L. Wang from Taiwan. Allspeakers gave very nice lecturesHighlights of the Programs -›› 24

Calabi Flow, Contemporary Mathematics,Vol 367, 17-42, AMS, 2005.[8] S.-C. Chang, The 2-Dimensional CalabiFlow, Nagoya Math. J. Vol. 181 (2006),63-73[9] S.-C. Chang and C.-T. Wu, The Fourth-Order Q-Curvature Flow on Closed 3-Manifolds, Nagoya Math. J., Vol. 185(2007), pp 1-15 (to appear).[10] J.-H. Cheng, S.-C. Chang, H.-L. Chiu, Afourth order curvature flow on a CR 3-manifold, Indiana UniversityMathematical Journal, to appear, 2007.[11] C.-T. Wu, S.-C. Chang, The Fourth-OrderQ-Curvature Flow on Closed 3-Manifolds, Nagoya Math. J., pp 1-15,2007.2. Harmonic Function and Harmonic MapTheory.The classical de Rham-Hodge theory,which relates the cohomology group of acompact manifold to its space of harmonicforms, is one of the most fundamental theoriesin modern mathematics. With the help of ananalysis technique first introduced by Bochner(called Bochner technique), the theory hasyielded many interesting and important resultsrelating topology to geometry. Even thoughthe theory is no longer valid on noncompactmanifolds, the idea of using analysis tounderstand the interaction between topologyand geometry is pivotal and fruitful ingeometric analysis. Basic Principle ; Tocontrol a metric. find a function that we knowwell and give a gradient or higher-orderestimate of this function. These functionsshould be defined by geometric construction ordifferential equation arise in geometry.In connection with Prof. Peter Li (UCI) andProf. Jiaping Wang (CUHK) , manyfundamental and important works are donesuch as[1] J.-H. Cheng, J.-F. Hwang, A. Malchiodi,and P. Yang, Minimal surfaces inpseudohermitian geometry and theBernstein problem in the Heisenberggroup, Annali della Scuola NormaleSuperiore di Pisa, Classe di Scienze (5),4(2005), 129-177.[2] J.-T. Chen, C.-J. Sung, Dimension estimateof polynomial growth harmonic forms,Journal of Differential Geometry, Volume73, Number 1, p. 167-183, 2006.[3] Roger Chen, Jiaping Wang, Polynomialgrowth solutions to higher-order linearelliptic equations and systems. Pacific J.Math. 229, no. 1, 49-61, 2007.3. Geometric Strucures :There are very important fields such thatEinstein manifolds and their moduli space,Conformal and CR geometry, Complexgeometry, Special Lagrangian Submanifoldsand Mirror Symmetry, Manifolds of specialholonomy and their submanifolds.In connection with Prof. S.-T. Yau (HarvardUniversity), Prof. Alice Chang (PrincetonUniversity), Prof. Der-Chen Chang(Georgetown University), Prof. Jianguo Cao(University of Notre Dame), Conan Leung(CUHK) and M.-T. Wang (ColumbiaUniversity), many fundamental and importantworks are done such as.[1] S.-J. Kan, Complete hyperbolic Steinmanifolds with prescribed automorphismgroups, Commentarii MathematiciHelvetici, no. 82, 371-383, 2007.[2] S.-J. Kan, Some complete invariant metricsin Grauert tubes, Mathematical ResearchLetters, no. 14, 205-220, 2007.[3] H.-L. Chiu, Compactness ofpseudohermitian structures with integralbounds on curvature, Math. Ann, vol.334 ,p.111-142, 2006.[4] H.-G. Chan, Simply-connectednonpositively curved surfaces in R^3.Pacific Journal of Mathematics. 223, 1-4,2006.[5] Tsai, Y., Xia, E., Non-Abelian localinvariant cycles. Proc. Amer. Math. Soc.135 (2007), no. 8, 2365-267.[6] Joshi, K., Ramanan, S., Xia, E., Yu, J., Onvector bundles destabilized by Frobeniuspull-back. Compositio Math. 142 (2006),Highlights of the Programs -›› 26

616-630.[7] Ho, N., Jeffrey, L., The volume of themoduli space of flat connections on anonorientable 2-manifold, Comm. Math.Phy. 256 (2005), 539-564.[8] Ho, N., Liu, M., Connected Components ofthe Space of Surface GroupRepresentations II, Inter. Math. Res.Notices 16 (2005), 959-979.[9] Chiang, R., Complexity one HamiltonianSU(2) and SO(3) actions. Amer. J. Math.127 (2005) 129-168.[10] Ho, N., The real locus of an involutionmap on the moduli space of flatconnections on a Riemann surface, Inter.Math. Res. Notices 61 (2004), 3263-3285.4. Mathematical Aspects of General Relativity.The CR Yamabe problem is to find acontact form on a close CR manifold withconstant Tanaka-Webster curvature. In serialpapers, D. Jerison and J. Lee initiated thestudy of this problem . They confirmed the CRYamabe problem in case of the CR Yamabeconstant is less than the one for a standard CRsphere. Their methods can be compared to thepartial completion of the proof of RiemannianYamabe problem by T. Aubin. By thepseudohermitian analogue, the remainingcases should be solved using a CR version ofthe positive pseudohermitian-mass conjecturewhich is not available at this present stage ofresearch.In connection with Prof. S.-T. Yau (HarvardUniversity), Prof. J. Isenberg (University ofOregon) and Prof. X. Chang (ChineseAcademy Sciences), a few fundamental andimportant works are done such as[1] H.-G. Chan, Embedding negatively curvedinitial data of black-hole collisions in R3.Classical and Quantum Gravity., 23, 225-234, 2006.27 ‹‹- Highlights of the Programs

D.5 Lie Theory and Related Algebra at NCTS 2004-2007Coordinator: Meng-Kiat Chuah (National Tsing Hua University)Part I : Background and Activities inthe Programie Theory at NCTS is understood in abroad sense. This includes thestructure theory and representation theory ofLie groups, Lie algebras and vertex operatoralgebras, and related applications in numbertheory and ring theory. Research programs inthis area are very active in NCKU, NTHU andAcademia Sinica.The researchers jointly organize a weeklyLie Theory Seminar. Since 2004, about 30visitors have come from the USA, Japan,Korea, Germany, Hong Kong and Australia.Members of this focus group have won theOutstanding Research Award (NSC), Wu Ta-You Award (NSC), Academic Award (TMS),Young Mathematician Award (TMS), and theAcademia Sinica Young Investigator Award.Local Focus GroupS. J. Cheng (Sinica), M. K. Chuah(NTHU), P. Y. Huang (NCKU), W. F. Ke(NCKU), C. H. Lam (NCKU), N. Lam(NCKU), C. F. Nien (NCKU), S. Y. Pan(NTHU). Presently there are 3 PhD students inthis group.Post DoctorC. C. Hu (NTHU 2006-07).Frequent VisitorsM. Chebotar (Kent State), Koichiro Harada(Ohio State), J. S. Huang (Hong Kong U. Sci.Tech.), King Fai Lai (Sydney), HirokiShimakura (Chiba U.), Hiroshi Yamauchi(Aichi U. of Education).Short Term VisitorsT. Arakawa (Nara Woman U.), S. Ariki(RIMS Kyoto), B. Griess (U. Michigan), A.Huckleberry (U. of Bochum), R. Inoue (U.Tokyo), S. J. Kang (Seoul National U.), H.Kiechle (Hamburg), S. Kumar (U. NorthCarolina-Chapel Hill), J. H. Kwon (Seoul), L.Ling (Iowa State), A. Matsuo (U. Tokyo), V.Mehta (Tata Institute), J. Meyer (Free State,South Africa), D. Nakano (U. Georgia), R. Ng(Iowa State), B. Parshall (U. Virginia), L. Scott(U. Virginia), W. Wang (U. Virginia), H.Yamada (Hitotsubashi), T. Yamasaki (TohokuU.), R. B. Zhang (U. Sydney).Advanced Courses and Seminars• Introduction to Framed vertex operatoralgebra, Aug, 2004:• This course is an 8-hour mini course givenby H. Yamauchi. The main aim is tointroduce the beautiful construction ofMiyamoto of the Moonshine vertex operatoralgebra using codes.• Groups of even order, Mar 2005:• It is a 6-hour mini course given by KoichiroHarada. Its aim is to introduce the idea ofBrauer for classifying finite simple groups.• Lie Theory Seminar, April 2007-June 2007:• Weekly seminar given by S. J. Cheng, C. H.Lam, M. K. Chuah, S. Y. Pan and somegraduates students. The Topics of the seminarinclude character formula of Lie algebras,vertex operator algebras, extended Vogandiagrams, and nilpotent orbits of semisimpleLie algebrasConference and Workshops• International Conference of Algebra inMemory of Kostia Beidar, Mar 6-12, 2005 atNCKU. Organizers: W. F. Ke, Y. Fong and P.H. Lee.Highlights of the Programs -›› 28

• Speakers: E. Zemanov, L. Small, LeonidMakar-Limanov, E. Puczyloski, R. R.Wisbauer, T. Arakawa• Algebraic Aspects of Lie Theory andGeometry, Third Pacific Rim ConferenceSpecial Session, Fudan U, Shanghai, July2005. Organizers: S. J. Cheng.• Representation Theory, First AMS-TMSJoint Meeting Special Session, Tunghai U,Taichung, December 2005. Organizers: S. J.Cheng, B. Parshall and W. Wang.• Algebraic Aspects of Lie Theory, AcademiaSinica, December 2007. Organizers: S.-J.Cheng and W. Wang.• Under planning: NCTS Winter School inRepresentation Theory, Hsinchu, January 25-29, 2008. Organizers: M. K. Chuah and J. S.Huang.International CooperationsS.-J. Cheng visited the University ofVirginia for one year in 2003-2004. During hisstay there he gave one seminar talk in theInfinite-dimensional algebra seminar at MIT,and the Lie groups and geometry seminar atthe CUNY in New York. He gave an invitedtalk at the International Conference onRepresentation Theory III in Chengdu in theJuly 2004, and was asked to organize a specialsession at the Third Pacific Rim Conference inFudan University, Shanghai in July 2005. Hevisited the University of Sydney in the August2005, and the University of Virginia inNovember 2006. He is scheduled to give aninvited talk at the International Conference onRepresentation Theory IV in Tibet in July2007. He is scheduled to visit the University ofVienna in August 2007, and the University ofVirginia in October 2007.M. K. Chuah attends the Summer Schoolon Representation Theory held at the ChernInstitute of Mathematics (Nankai University,Tianjin) in 2006 as a guest, and in 2007 as aninvited lecturer. This leads to a collaborationwith J. S. Huang on symmetric spaces. He isinvited to give a seminar talk on Vogandiagrams at the conference Sapporo Lectureson Representations in Lie Theory (HokkaidoUniversity) in August 2007. He is also aninvited speaker at the December 2007 ICCMin Hangzhou, China.In the winter 2005, C.H. Lam visitedUniversity of Tsukuba. During this visit, hewas one of the active members of the Komabagroup theory seminar in Tokyo, whosemembers include M. Kitazume (Chiba), A.Matsuo (Tokyo), M. Miyamoto (Tsukuba), H.Shimakura(Chiba), H. Yamada (Hitotsubashi),H. Yamauhci (Tokyo) and also gave severalseminar talks. In addition, he has made manyshort term visits to Japan and was an invitedspeaker in several conferences in Kyoto,Hamamachi, Nara and Tokyo.In January 2007, S.-Y. Pan attended TheAnnual Meeting of American MathematicsSoceity and gave an invited talk in the sectionof representation theory. Then he visitedLouisiana State University for a few days. Heis going to have a jointed project on nilpotentorbits of semisimple Lie algebras with H. Heof LSU.Part II: The Accomplished and theAnticipationsSelected publications of the local focusgroup since 2004:[1] M. A. Chebotar, W.-F. Ke, P.-H. Lee. OnBresar-Semrl conjecture and derivations ofBanach algebras. Quart. J. Math. 57(2006), 469-478.[2] M. Chebotar, W.-F. Ke, P.-H. Lee, R. B.Zhang. On maps preserving zero Jordanproducts. Monatsh. Math. 149 (2006), 91-101.[3] M. Chebotar, W.-F. Ke, P.-H. Lee. On mapspreserving square-zero matrices. J.Algebra 289 (2005), 421-445.[4] S.-J. Cheng, N. Lam and R. B. Zhang,Character Formula for infinite-dimensionalunitarizable Modules of the general linearSuperalgebra, J. Algebra 273 (2004), No.2, 780-805.[5] S.-J. Cheng and R. B. Zhang, HoweDuality and Combinatorial CharacterFormula for Orthosymplectic Lie29 ‹‹- Highlights of the Programs

Superalgebras, Advances Math. 182(2004), No. 1, 124-172.[6] S.-J. Cheng, W. Wang and R. B. Zhang, AFock Space Approach to RepresentationTheory of osp(2|2n), TransformationGroups 12 (2007), No. 2, 209-225.[7] S.-J. Cheng, W. Wang and R. B. Zhang,Super Duality and Kazhdan-LusztigPolynomials, Trans. Amer. Math. Soc., toappear.[8] M. K. Chuah, Symplectic induction andsemisimple orbits, Bull. London Math.Soc. 37 (2005), 446-458.[9] M. K. Chuah, The direct integral of someweighted Bergman spaces, Proc. Edinb.Math. Soc. 50 (2007), 115-122.[10] M. K. Chuah and C. C. Hu, A quick proofon the equivalence classes of extendedVogan diagrams, J. Algebra 313 (2007),824-827.[11] M. K. Chuah, Geometric quantization andZuckerman models of semisimple Liegroups, Forum Math., to appear.[12] C. Dong, R. L. Griess and C.H. Lam,Uniqueness results of Frenkel-Lepowsky-Meurman's moonshine vertex operatoralgebra, Amer. J. Math. 129, No. 2(2007), 583 609.[13] C.H. Lam and H. Yamauchi, On thestructure of framed vertex operatoralgebras and their pointwise framestabilizers, to appear in Comm. in Math.Phys.[14] C.H. Lam, S. Sakuma and H. Yamauchi,Ising vectors and automorphism groups ofcommutant subalgebras related to rootsystems, Math. Z. Vol. 255, No.3, Mar.2007, 597-626.[15] C.H. Lam and M. Miyamoto, NiemeierLattices, Coxeter elements and McKay'sE 8 observation on the Monster simplegroup, Inter. Math. Res. Not., Vol 2006(2006), 27 pages.[16] N. Lam and R. B. Zhang, Quasi-finitemodules for Lie superalgebras of infiniterank, Trans. Amer. Math. Soc. 358(2006), No. 1, 403-439.[17] S. Y. Pan, Local theta correspondences forsmall unitary groups, Trans. Amer. Math.Soc. 358 (2006), 1511-1535.One focus of the research group, includingS.-J. Cheng, W. Wang, and R. B. Zhang, is thestudy of the representations of Lie(super)algebras. In [5] Howe duality is appliedto the study of Lie superalgebras wherecharacters of certain oscillator representationsof the orthosymplectic Lie superalgebra arecomputed. One remarkable consequence is thata wide class of irreducible characters of theseLie superalgebras are determined by thecharacters of certain infinite-dimensional Liealgebras. In [7] a precise connection betweenthe Kazhdan-Lusztig theories of the generallinear Lie superalgebra and the general linearalgebra is formulated and proved. It followsthat their respective representation theories (incertain categories) are equivalent. Such aconnection between Lie algebras and Liesuperalgebras has been observed for the veryfirst time. In [6] a certain q-deformed Fockspace is constructed whose combinatorics ofstandard monomial, canonical and dualcanonical bases, completely determined thefinite-dimensional representation theory of theLie superalgebra osp(2|2n).Motivated by the works of Bloch andOkounkov who defined a certain refinedversion of the character for the infinitedimensionalgeneral linear algebra at levelone, S.-J. Cheng and his co-workers also founda remarkable closed form for their correlationfunction in terms of certain theta functions.This result is extended to higher positive andnegative levels, the correlation functions areexpressed in terms of certain q-hypergeometricseries.The papers [16] deals with therepresentation theory of central extensions ofthe infinite rank Lie superalgebras of type Aand OSP. The main result in the paper is theclassification of all irreducible highest weightquasi-finite modules.In the last few years, our groupin vertexoperator algebra has obtained severalimportant results. In spring 2004, C.H. Lam,Highlights of the Programs -›› 30

H. Yamada, H. Yamauchi began a project onstudying some mysterious connectionsbetween the Monster group and the affine E 8diagram, which was first observed by JohnMcKay 35 years ago. This collaboration leadsto works in which a vertex operator algebratheoretical explanation for McKay's E 8observation were given. After that, M.Miyamoto and C. H. Lam obtained a naturalexplanation for McKay's E 8 observation byusing some twisted construction of the Leechlattice [15]. Recently, C.H. Lam, H. Yamauchiand G. Hohn also began to study some similarrelations between affine E 7 and E 6 diagramswith the Babymonster group and the largestFisher group and a lot of progress has beenmade.In winter 2005, C. H. Lam visitedUniversity of Tsukuba, with the support ofJSPS. This visit ended up with severalsuccessful collaborations. On the structure offramed vertex operator algebras and theirorbifolds, C.H. Lam and H. Yamauchi showedthat all framed vertex operator algebras aresimple current extension of the correspondingcode vertex operator algebras, to appear inComm. in Math. Phys. [13]. Based on thisresult, C.H. Lam, H. Yamauchi and H.Shimakura started a program on classifyingholomorphic framed vertex operator algebrasof small central charges using binary codes.This work is still under progress but a simplecharacterization of the moonshine vertexoperator algebra has been obtained whichverifies a conjecture of Frenkel-Lepowsky-Meurman on the uniqueness of the moonshinevertex operator algebra. Around the same time,another characterization of the moonshinevertex operator algebra was also obtained byC. Dong, R. L. Griess and C.H. Lam under theassumptions that the algebra structure of theweight 2 space is isomorphic to the MonstrousGriess algebra [12]. In addition, S. Sakuma, H.Yamauchi and C.H. Lam have studied theIsing vectors inside the lattice type vertexoperator and their commutant [14]. Theyclassified all Ising vectors in . Moreover,they constructed many new vertex operatoralgebras whose full automorphism groups arealmost simple 3-transposition groups. Thiswork has also been generalized by H.Shimakura and C.H. Lam to the Leech latticevertex operator algebra.Problems on finite planar nearrings arestudied in a series of papers by K. I. Beidar,W.-F. Ke, H. Kiechle. Using representationtheory, W.-F. Ke, K.F. Lai and R.B. Zhang alsoderived a systematic construction method ofquantum error correcting codes whichgeneralizes, in particular, the Shor's 9-qubitcode.The theory of functional identity wasinvented about 10 years ago by Beidar andChebotar. Many important problems, such asthe Lie maps conjecture posted by Herstein,was solved completely by this method. Withthe same tool, many problems of linearpreserver problem were attached andconquered with success during the past fiveyears by the algebra group in National TaiwanUniversity and National Cheng KungUniversity [1, 2, 3].The main subject of Shu-Yen Pan s recentresearch is the L-functoriality of the local thetacorrespondence. In particular, he proves thatAdams/Harris-Kudla-Sweet s conjecture onthe Langlands parameters of the chain ofsupercuspidal representation obtained by theconservation principle of the local thetacorrespondence is true if these supercuspidalrepresentations have unipotent reduction.One research interest of M.-K. Chuah is thediagrammatic expression of involutions ofsimple Lie algebras, known as Vogan diagram.Several Vogan diagrams may represent thesame involutions, and in joint series of workswith C. C. Hu, e.g. [10], such diagrams aresort out. The other direction in which progressare made by Chuah is the study of relationsbetween group representations and symplecticgeometry, known as geometric quantization,carried out in [8], [9], [11].31 ‹‹- Highlights of the Programs

D.6 Mathematical Biology at NCTS 2004-2007Coordinator: Sze-Bi Hsu (National Tsing Hua University)Part I: Background and Activities inthe Programathematical Biology is aninterdisciplinary area betweenmathematicians, statisticians, computerscientists and biologists. Currently the mainsubject of the topical program of MathematicalBiology in NCTS is Population Dynamics.(Another important subject is Bioinformaticswhich is currently included in the TopicalProgram of Probability) In PopulationDynamics we limit our attentions toMathematical Ecology, MathematicalEpidemiology and Mathematical Physiology.In the traditional mathematical biology,mathematicians study the oversimplifiedmathematical models from biology withemphasis on their new mathematical propertiesbut with little feedback to biology. The modernmathematical biology however emphasizes thecollaborations with biologists. Usually themathematical models are more realistic andbut too complicate to do mathematical analysisand hence large scale scientific computationsare needed to explore more biologicalphenomenon.There are over 15 short term visitorsparticipating in the Mathematical Biologyprogram since 2004. They come forconference-workshops, and/or for a visit up toone month. Among them are the world leadingmathematical biologists e.g. S.Hubbell(U.Georgia), Hans Othmer (Minnesota), HalSmith (Arizona State),Mark Chaplan (Dundee,UK), Jiahong Wu (York, Canada).Local GroupS.B. Hsu (NTHU), C.W. Shih (NCTU),M.C. Li (NCTU), M.C. Lai (NCTU), T.W.Hwang (CCU), J.C. Tsai (CCU), Y.H. Hsieh(NCHU), C.C. Li (San John Polytech.), C.P.Lo (Providence), I.F. Sun (THU, Biology),Y.H. Tzeng (Academia Sinica, GenomicCenter).Post DoctorY.Y .Chen (NCTS 2007, Plant Biology)Frequent VisitorsYihing Du (U. New England, Australia),Lih-Ing Wu (Texas Tech.)Short Term VisitorsF.Brauer ( British Columbia), M. Chaplain(Dundee,UK),Y.S.Choi (Connecticut,USA), J.Glasser (US CDC, Atlanta), J.Lowengrub (UCIrvine), R. Lui (WPI, USA), S. Ma (PublicHealth, Singapore), A. Mogilner (UC Davis),H. Othmer (Minnesota), S. Riley ( Hong KongUniversity), H. Smith (Arizona State,USA),H.O.Walther (U. Giessen, Germany), J.H. Wu(York, Canada). P. Yan (Public Health Agencyof Canada), X. Zhao (Memorial U ofNewfounder, Canada)Advanced Courses in 2004-2007• Dynamics of Delays, Feb. 22-March 6, 2004,by Hans Otto Walther, New methods ofhomoclinic transversality is introduced forthe study of chaotic behavior of solutions ofthe delay differential equations.• Spatial Heterogeneous Mathematical Modelsin Population Biology, March 15-May 15,2004, by S.B. Hsu and C.P. Lo. This coursecovers maximal principle, comparisonprinciple, monotone methods for elliptic andparabolic PDE, logistic equation in PDEform, Predator-Prey system and competitionsystem in heterogeneous environment, blowupbehavior of elliptic PDE.Highlights of the Programs -›› 32

• Monotone Dynamical Systems, by Sze-BiHsu, Aug 1-Aug.31, 2006. This coursecovers ODE of cooperative systems as anexample of monotone flow, monotone flowin abstract space, Poincare-Bendixson likeTheorem for 3-dimensional competitivesystem, applications to reaction-diffusionequations, delay differential equations andmaps.• Reaction Diffusion System withApplications to Spatial Ecology, March 15-April 26,2007, by Yihong Du. This coursecovers classical and degenerate logisticmodel, classical diffusive competition andpredator-prey model, the degeneratecompetition model and predator-prey modeland their perturbations.• Spreading Speeds and Traveling waves formonotone semiflow with applications, April27-May 28, 2007, by Xiaoqiang Zhao. Thiscourse covers the estimate of the spreadingspeed for a traveling wave solution for areaction-diffusion systems with monotoneproperties.Undergraduate CourseMathematical Theory of MolecularEvolution, Spring semester of 2006, by Y.H.Tzeng. This course covers (i) Introduction topopulation genetics, (ii) Dynamics ofnucleotide substitution, (iii) Estimating thenumber of nucleotide substitutions betweensequence, (iv) Computation molecularbiology..Conferences and Workshops• Workshop of Mathematical Models andProblems in Cell Motility and TumorGrowth, Jan.11-19, 2006 at NCTS.Organizers: S.B.Hsu and R. Lui. Speakers:H. Othmer, A. Mogilner,M. Chaplain, J.Lowengrub,Y.S. Choi, R. Lui, J.L.Yang,,C.H. Lin, H. Ninomiya, S. McDougall.• Workshop on Mathematical Modeling ofInfectious Disease Epidemiology, May 31-June 2,2006 at NCTS. Organizers: S.B.Hsuand Y.H.Hsieh. Speakers: S. Ma, S. Riley,J.H.Wu, P.Yan, J. Glasser, F.Brauer, S.B.Hsu,Y.H.Hsieh.• Mini-Workshop on Mathematical Biology,May 9-10, 2007 at NCTS. Organizers:S.B.Hsu and H. Smith. Speakers: X. Zhao,H. Smith, S.B. Hsu, Y.H.Hsieh, T.W.Hwang,C.P.Lo,J.C. TsaiExchange Programs and InternationalCooperationsDuring 2002-2004, with the support fromNCTS fellowship, we sent Ph.D studentY.H.Tzeng to the department of Evolutionbiology and Ecology , University of Chicagoto do research of molecular evolution underthe supervision of Professor Wen-Hsiung Lifor two years. Now Dr. Tzeng is the firstmathematics Ph.D in Taiwan with the trainingin molecular evolution and bioinformatics. Heis currently working in the genomic Center inAcademia Sinica.Part II: The Accomplished and theAnticipationsSelected publications of the local groupsince 2004:[1] Y.H.Hsieh and S.B.Hsu et. Impact ofquarantine on the 2003 SARS outbreak: Aretrospective modeling study , J.Theoretical Biology 244(2007) 729-736.[2] S.B.Hsu and Lih-Ing Wu, The final size ofa SARS epidemic model withoutquarantine , JMAA 333(2007) 557-566.[3] Y.H. Hsieh and S.B.Hsu, On the role ofasymptomatic infection in transmissiondynamics of infectious disease, to appear inBulletin of Mathematical Biology 2007.[4] Y.H.Hsieh and S.B.Hsu Modelingintervention measure and severitydependent public response during severeacute respiratory syndrome outbreak,SIAM J. Appl. Math. 66,No.2 (2006) 627-647.[5] S.B.Hsu and C.C.Li, A discrete delaymodel with plasmid-bearing plasmid freecompetition in a chemostat, Discrete andContinuous Dynamical Systems, vol5,No.3, (2005) 699-718.33 ‹‹- Highlights of the Programs

[6] Y.H.Du and S.B.Hsu, A diffusive predatorpreymodel in heterogeneous environmentJournal of Differential Equations 203(2004) 331-364.[7] Y.H.Hsieh, S.B.Hsu and Cathy Chen. Thesevere Acute Respiratory Syndromeoutbreak in Taiwan: Lesson to be learn,Emerging Infectious Disease (2004) vol.10, No.2 ,201-206.[8] Tzeng Y.H. ,R.Pan,W.H.Li, Comparison ofthree methods for estimating rates ofsynonymous and nonsynonymousnucleotide substitution, Mol. Biol.Evol.(2004) 21(12) 2290-2298.[9] Shin S.H., W.Karlowski, R.Pan,Y.H.Tzeng, K.F.Mayer and W.H.Li,Comparative Analysis of the receptor-likekinase family in Arabidopsis thaliana andrice, Plant Cell (2004) 16,1220-1234.[10] J.C.Tsai and J.Sueyd,Existence andstability of traveling waves in bufferedsystems, SIAM J.Appl. Math. Vol66,No.1,pp.237-265 (2005).[11] J.S.Guo and J.C.Tsai, The asymptoticbehavior of solutions of the bufferedbistable system, Journal of MathematicalBiology 53(2006) 179-213.[12] J.C.Tsai, Asymptotic stability of travelingwave front in the buffered bistablesystem, SIAM J.Math.Analysis39(2007)pp.138-159.In additional to the training in ODE, PDE,Dynamical Systems, we encourage ourgraduate students to take courses in lifescience departments and learn how tocommunicate with biologists. Currently we askthe students to have solid training inmathematics and expect them to learn somemathematical modeling in biology.The topical program of MathematicalBiology usually joins with other topicalprograms ,e.g., PDE , Dynamical Systems,Probability. We sometimes invite localbiologists or physicists to give talks on theirwork related to mathematical modeling.In Mathematical Ecology, we have a closecollaboration with ecologist Professor I-FangSun of Tung-Hai University on the modelingon Ecology and Disease. Recently we hire apost doctor Y.Y.Chen ,a Ph.D of Plant Ecologyfrom University of Georgia. We expect tolearn more biology and to cooperate with heron constructing mathematical modeling ofSpatial Ecology and Neutral Theory inEcology.In Mathematical Epidemiology, S.B.Hsuand Y.H. Hsieh complete several modelingwork and their mathematical analysis on theoutbreak of SARS in Taiwan. Currently wehave finished the work on the mathematicalmodels of Avian Flu .We plan to study thenosocomial infection in hospital with medicalpeople.In Mathematical Physiology, J.C.Tsaistudies the wave propagation of increasedcalcium concentration of cells in excitablesystem. C.P.Lo and his collaborators inTaichung Veteran Hospital study themathematical models of hearts and do somecomputation work.We anticipate in the future we have morecollaborations with biologists to constructmathematical models for the importantproblems arising from biology.Highlights of the Programs -›› 34

D.7 Number Theory at NCTS 2004-2007Coordinator: Jing Yu (National Tsing Hua University)Part I: Background and Activities inthe Programumber Theory at NCTS is understoodin a broad sense, including traditionalalgebraic number theory, arithmetic geometryand automorphic representations. Diophantinegeometry and arithmetic of algebraic functionfields are also among the main interests. Aregular number theory seminar is run at NCTSweekly, including lectures given by visitors toNCTS and reports on research results given bymembers of the local focus group.There are over 30 short term visitorsparticipating in the number theory programsince 2004. They come for conferencesworkshops,and/or for a visit up to one month.Among them are the world leading numbertheorists e.g. T. Saito (Japan), G. Wüstholz(Switzerland), H. Darmon (Canada), D.Brownawell (USA), J. Silverman (USA), andF. Beukers (the Netherlands). They, as well asthe long term visiting scientists, are naturallyour consultants on developing researches ofnumber theory in Taiwan.The frequent visitors are 5 mathematicianswho visited NCTS more than once in the past,and had or currently have joined researchprojects with members of the local focusgroup. For a report in this respect, see Part II.In 2006, 3 members of this focus groupreceived awards for their research works: oneWu Ta-You research award from NSC, andtwo young scholar's awards from theAcademia SinicaLocal Focus GroupJ. Yu (NCTS Center Scientist and NTHU),Y.-M. J. Chen (NCU), L.-C. Hsia (NCU), M.-G. Leu (NCU), A. Li (Fu Jen U.), H.-C. Li(NTNU), C.-H. Lin (NCKU), C. Nien(NCKU), S.-Y. Pan (NTHU), J. T.-Y.Wang(Academia Sinica), W.-C. Yao (TMUE), Y.Yang (NCTU), C.-F. Yu (Academia Sinica).Presently there are also 10 Ph.D. students inthis group, from NTHU, NCU, and NCTU.Long Term Visiting ScientistsC.-L. Chai (U. Penn.), 2004 Springsemester. Winnie W.-C. Li (Penn. state U.),2006/07 whole year as center scientist atNCTS.Post DoctorsC.-J. Wang (NCTS 2006-), Y.-C. Yi (NCTS2005-07), C.-C. Li (Academia Sinica 2005-07), C.-Y. Chang (NCTS 2007-).Frequent VisitorsJean-Yves Briend (Provence), W.-T. Kuo(U. Waterloo), M. Papanikolas (Texas A & MU.), J. Tilouine (Paris Nord), J.-K. Yu (PurdueU.).Short Term VisitorsA. Ashikhmin (Bell Lab.), F. Beukers (U.Leiden), G. Boeckle (U. Essen), N. Boston (U.Wisconsin), P. Bundschuh (Köln), R.Calderbank (Princeton U.), H.-H. Chan (NU.Singapore), W. Cherry (North Texas U.), H.Darmon (McGill U.), A, Garcia (IMPA), A.Hoshi (Waseda U.), M-D. Huang (USC), M.Kim (Purdue U.), K. Komatsu (Waseda U.),J.Korman (U. Toronto), K. F. Lai (U. Sydney),Y.-R. Liu (U. Waterloo), L. Long (Iowa stateU.), W. Luo (Ohio state U.), H. Maharaj(Ciemson U.), J. V. Maillot (Paris 7), J.MaKay (Concordia), K. Miyake (Waseda U.),Y. Mizusawa (Sophia U.), D. Ramakrishnan(Caltech), W, Raskind (USC), T. Saito (Tokyo35 ‹‹- Highlights of the Programs

U.), D. Savitt (U. Arizona), J.Silverman(Brown U.), D. Thakur (U. Arizonz), G.Wüstholz (ETH), T. Yang (U.Wisconsin).Advanced Courses in 2004-2007• Modular forms and Galois representations,Fall 2006. This course is given by WinnieW.-C. Li and C.-F. Yu. It s aim is theconnection between modular forms andGalois representations. Starting point is theEichler-Shimura relations, then Deligne'sgeneralization from weight two to higherweight modular forms. The reverse direction,by Wiles, Taylor, etc, giving criteria for l-adic representations to be modular is alsodiscussed.• Topics on Diophantine geometry, Fall 2004.Lecturers includes : L.-C. Hsia, J. T.-Y.Wang and J. Yu. This course covers : heights,Mordell-Weil theorem, abelian varieties,Roth's theorem, emphasizing geometricmethods in number theory.• Topics on number theory and representationtheory, Spring semester and fall semester2004. Lecturers includes : J. Yu, L.-C. Hsia,C.-J. Wang, C.-F. Yu, J. T.-Y.Wang, Y.-M. J.Chen. Themes are : Artin's L-functions,modular forms, Weil representations, Heckecharacters, Maass forms and automorphicrepresentations of GL(2), Half-integralweight modular forms.• Topics in one complex variable, Spring2004. Lecturers includes : J. Yu, J. T.-Y.Wang, L.-P. Tee and Y. Yang. This course isaimed at interactions with number theory,e.g. Nevanlinna theory, transcendence theoryand analytic number theory.Conferences and Workshops• Conference on Galois representations andfunction field arithmetic, May 14-17, 2007 atNCTS. Organizers : Winnie W.-C. Li and J.Yu. There are 10 speakers from abroad.• Workshop on Iwasawa theory andautomorphic representations, September 4-7, 2006 at NCTS. Speakers : K. komatsu, Y.Mizusawa, C.-J. Wang and J. Yu.• Workshop on coding theory, June 28-July 23,2004, at NTU. Organizers : M.C. Kang(NTU) and Winnie W.-C. Li. There are 6speakers from abroad.• Workshop on arithmetic and algebraicgeometry, number theory and representationtheory, December 30/31, 2004 and January6/7, 2005 at Academia Sinica and NTU.Organizer: C.-F. Yu. Speakers : Ching-LiChai, Chien-Jan Wang, W. Cherry, andJungkai Chen.• Workshop on arithmetic geometry andrepresentation theory, January 6-8, 12-13,2004 at NCTS. Organizer: J. Yu. Speakers:C.-L. Chai, C.-J. Wang, T. Yang, and C.-F.Yu.Exchange Programs and InternationalCooperationsBesides individual visits by members ofour focus group to centers and universities inU.S.A., Canada, Germany, France, England,Italy, Spain, Japan, China, Hongkong, Korea,Vietnam, we have strengthened cooperationswith three countries:Japan. January 2005. Group consisted of J.Yu, L.-C. Hsia, C.-F. Yu, S.-Y. Pan, Y.-M. J.Chen and a Ph. D. student visited Japan fortwo weeks, being invited to Kyoto U., NagoyaU., Tokyo U., speaking at their number theoryseminars and attending conference onautomorphic forms and automorphic L-functions at RIMS. This visit was sponsoredby grant from the Minister of Education. InDecember 2005, Y.-C. Yi and a Ph. D. studentwere invited to RIMS conference on algebraicnumber theory, December 2006, Y. Yang wasinvited to RIMS conference on algebraicnumber theory. March 2006, J. Yu, W.-C. Yaoand a Ph.D. student were invited to annualalgebraic number theory conference at WasedaU., March 2007, L.-C. Hsia and a Ph.D.student were invited to annual algebraicnumber theory conference at Waseda U. Allthe graduate students participating in theseexchangeswere supported by Minister ofEducation grant.France. July 17-29, 2006, Asian-Frenchsummer school in algebraic geometry andnumber theory, at IHES. Organizers : J.-B.Bost, J. P. Bourguignon, J. M. Fountaine, L.Highlights of the Programs -›› 36

Lafforgue, N. B. Châu, M. Kim, M. Levine, T.Saito (Japan), S. Ramdorai (India), L. Fu(China), N. Mok (Hong Kong), C.-F. Yu(Taiwan). Taiwan participating group consistedof 9 graduate students, and H.-W. Lin, S.-Y.Pan, J.- H. Teh, C.-L. Wang, C.-F. Yu, and J.Yu. Also in summer 2004, J. T.-Y. Wang, J.Yu, Y.-M. J. Chen and L.-C. Hsia were invitedto visit France, joining conferences andworkshops at Clermont-Ferrant, Toulouse andMarseille. Furthermore there are two Ph.D.students from France (Paris 7 and Paris nord)joined 2005 summer research program innumber theory at NCTS.Korea. September 2004, J. Yu, A. Li, and W.-C. Yao were invited to visit KIAS and KAIST.February 2007, J. Yu and two Ph.D. studentswere invited to KAIST. S. Hahn, Bae (Korea),(China), Kaneko (Japan), J. Yu (Taiwan) areorganizing an East Asia number theoryconference at Taejeon, Korea, January 21-242008.Student's Seminars and SchoolsSince 2004 each year we have one weekwinter school and one week summer school onvarious topics in number theory for graduatestudents, sponsored by Minister of Educationgrant (national chair in science) and NCTS,usually this is taken place at a conference siteoutside NCTS. In these schools, about half ofthe talks are presented by Ph. D. students.There are also monthly special day programsand weekly student's seminars during thesemesters at NCTS. Every summer, besidesthe summer school, there is also a summerprogram for graduate students and advancedundergraduates interested in number theory,and participating students (about a dozen eachsummer) are guided by professors from thefocus group. These students also receivepartial financial support from NCTS during thesummere period.In 2005/06, a special efforts had been madeon organizing a preschool for the IHES Asian-French summer school in algebraic geometryand number theory July 2006. This preschoolselected the 9 students who attended the IHESinternational program from Taiwan, and didbackground preparations in algebraicgeometry, modular forms and automorphicrepresentation theory.We have also supported travels of Ph.D.students to join selected summer/winterschools, or workshops abroad : 1 student toClay institute summer school in arithmeticgeometry 2006, 2 students in 2004, 1 in 2005,and 3 in 2007 to the Arizona arithmeticgeometry winter school, 2 students to theFields institute summer school in 2006, 1student to MSRI Diophantine geometryworkshop in 2006, 2 students to the PAMQ2007 school on Langlands and geometricLanglands program in Guanzhou, and 2students to 2007 ICTP summer school onautomorphic forms and Shimura varieties atTriesta. All of these students applied (mostlyreceived) local support from the organizers ofthese international programs.Part II: The Accomplished and theAnticipationsSelected publications of the local focusgroup since 2004 :[1] Ta Yhi Haoi An and J. T.-Y. Wang, Uniquerange sets and uniqueness polynomials foralgebraic curves, Trans. A.M.S. 359(2007), 937-964.[2] Ta Yhi Haoi An and J. T.-Y. Wang, Aneffective Schmidt's subspace theoremfor non-linear forms, J. of NumberTheorey, to appear 2007.[3] M. Baker and L.C. Hsia, Canonical height,transfinite diameters, and polynomialdynamics, J. reine angew. Math. 585(2005), 61-92.[4] C.-J. Chang and J. Yu, Determination ofalgebraic relations among special zetavalues in positive characteristic, to appearin Adv. Math. 2007.[5] Y.-H. Chen, Y. Yang and N. Yui,Monodromy of Picard-Fuchs differentialequations for Calabi-Yau threefolds, toappear in J. reine angew. Math. 2007[6] Y.-M. J. Chen and J. Yu, On primitive rootsof elliptic curves with complex37‹‹- Highlights of the Programs

multiplication, Journal of Number Theory114 (2005), 66-87.[7] Y.-M. J. Chen and J. Yu, On class numberrelations in characteristic two, toappear in Math. Zeit. 2007[8] Min Ru and J. T.-Y. Wang, A second maintheorem on parabolic manifolds,Asian J. Math. 9 (2005), 349-371.[9] L.-C. Hsia and J. T.-Y. Wang, Wronskians,and the ABC theorem for higherdimensional function fields of arbitrarycharacteristic, Trans. A.M.S. 356 (2004),No.7, 2871-2887.[10] Y. Yang, On differential equationssatisfied by modular forms, Math. Zeit246 (2004), 1-19.[11] Y. Yang, Defining equations of modularcurves, Adv. Math 204 (2006), 481-508.[12] C.-F. Yu, Irreducibility of the Siegelmoduli spaceswith parahoric levelstructures. Int. Math. Res. Not. 48 (2004),2593-2597.[13] C.-F. Yu, On the slope filtration of certainShimura varieties. Math. Zete. 251(2005), 859-873.[14] C.-F. Yu, The supersingular loci and massformulas on Siegel modular varieties.Doc. Math. 11 (2006), 449-468.[15] C.-F. Yu and J. Yu, Mass formula ofsupersingular Drinfeld modules, C. R.Acad. Sci. Paris, Ser. I 338 (2004), 905-908.[16] J. Yu and Q. Yue, On the density of 4-ranks of tame kernels for quadratic fields,J. reine angew. Math. 567 (2004), 151-173.In the direction of transcendence theory,particularly motivic transcendence theory inpositive characteristic which was firstdeveloped twenty years ago by J. Yu, breakthroughs have been made in the last few years(cf. Bourbaki seminar March 2007 by F.Pellarin). In 2004 summer, M. Papanikolasvisited NCTS writing up his NCTS preprint(05-1-19, to appear in Invent. Math.) onalgebraic independence of Carlitz (rank one)logarithms. Extending this to Carlitzpolylogarithms, C.-Y.Chang and J. Yusucceeds in 2005 to determining all thealgebraic relations of Carlitz zeta values atpositive integers (cf [4], to appear in Adv.Math.), completely settles a 70 years oldproblem. Later on Papanikolas revisited NCTSat end of 2005, and C.-Y. Chang visitedPapanikolas during 2006 under NSFscholarship, results of this collaboration (inpreparation and in preprint) establishes thealgebraic independence for rank two Drinfeldlogarithms, and also determines all thealgebraic relations among families of Carlitzzeta values (as constant fields varies in thesame characteristic). This collaboration willcontinue for years to come, targeting at theanalogue of Schanuel conjecture for arbitraryDrinfeld modules, and determining algebraicrelations of all zeta values, Gamma values, etc,connected with global function fields.After the Crelle paper [3] by Baker-Hsia onadelic polynomial dynamics whichsuccessfully generalizes Bilu's equidistributiontheorem, arithmetic dynamics is becoming oneof the major lines in Diophantine geometry weare interested in. J. Silverman and L.-C. Hsiais collaborating and organizing a workshop atAIM in January 2008 on this topic. Anotherdirection is the interaction of Diophantinegeometry with Nevanlinna theory, in particularvarious versions of Schmidt's theorem, and theABC theorem in the function field case (cf.[1], [8] for example). J. T.-Y. Wang have beencollaborating with several international expertson this subject for years, P. Wong, W. Cherryand M. Ru made substantial contributions(supported in the large part by AcademiaSinica). They are organizing a program atFields Institute in 2008.In summer 2004, Y. Yang, as NCTS fellow,visited N. Yui in Canada. This begins asuccessful collaboration on the monodromy ofhypergeometric differential equations, and leadto the fascinating paper [5] to appear in Crelle,about the monodromy of Picard-Fuchdifferential equations and Calabi-Yauthreefolds. Y. Yang is an expert on findingdefining equations for modular curves (cf. [9]),and connecting modular forms withHighlights of the Programs -›› 38

differential equations. Those conjectures in [5]will undoubtedly lead to many interesting andimportant developments in the near furure.Supersingular abelian varieties andsupersingular Drinfeld modules are of specialarithmetic interests. The classical massformula for these objects goes back toDeuring-Eichler, for which [14] is a farreachinggeneralization. C.-F. Yu is now anexpert in writing down these beautifulformulas in various settings, e.g. in [15] theresulting formula is for arbitrary rank DrinfeldA-modules. In recent years, C.-L. Chai and C.-F. Yu have also been working on the Heckeorbits problems on Hilbert modular varieties(in preprint and in preparation). This result hasinterest in its own right, as it is a PEL-typeanalogue of the Hecke orbit problem for Siegelmodular varieties investigated by Chai andOort, but it also plays an important reductionstep in the orignal Siegel situation. This jointwork has been included in as part of Chai sICM 2006 report.The paper [7] by Y.-M. J. Chen and J. Yuconcerns arithmetic in characteristic two. Itfills in a gap in the literature and complementsthe well-known thesis of E. Artin where onlyodd characteristic is treated. For functionfields, approaches to even characteristic can bequite different from the odd characteristiccase. The other more traditional problemsstudied by members of the group include theprimitive roots problem for commutativealgebraic groups and Drinfeld modules (cf.e.g. [6]), and the density problem of 4-ranks oftame kernels for quadratic fields (cf. 16]).Finally representation theory relating tonumber theory is a relative recent researchdirection to us. Representations of algebraicgroups over local fields is one focus. Thetacorrespondence over local fields as well asover global fields is another focus, e.g. worksby S.-Y. Pan. We certainly want to putLanglands program within our sight, andstudies automorphic representations overnumber fields as well as function fields.Besides probing on representations theory ofclassical groups, another goal is to make moreuse of automorphic representations as tool toour exploring of function field arithmetic.39 ‹‹- Highlights of the Programs

D.8 Optimizations and related Analysis at NCTS 2004-2007Coordinator: Soon-Yi Wu (National Cheng Kung University)Part I(A) OptimizationBackground and Activities inthe Programptimization at NCTS is understood ina broad sense, including traditionaloptimization theory, mathematicalprogramming and operational research. Aregular optimization seminar is run at NCTS,including lectures given by visitors to NCTSand reports on research results given bymembers of the local focus group.There are short term visitors participatingin the optimization program since 2004. Theycome for conferences-workshops, and/or for avisit up to one month. Among them are theworld leading optimization theorists, e.g.M.Fukushima (Japan), T. H. Jongen(Netherlands), E. Polak (USA), and Liqun Qi(Hong Kong). They, as well as the long termvisiting scientists, are naturally our consultantson developing researches of optimization inTaiwan.(B) AnalysisThe Analysis program covers mainlyfunctional analysis, operator theory, nonlinearanalysis and convex analysis, and theirapplications. Our major interests include:1. Banach manifolds and Jordan structuretheory.2. General theory of operator algebras andoperator spaces.3. General theory of linear preservers,composition operators, Jordanhomomorphisms and Lie homomorphismson function modules and operator algebras,as well as, general algebras and rings.4. Hankel and Toeplitz operators and theirspectral theory.5. Degree theory, optimization, and variationalproblems in infinite dimension.Local Focus GroupSoon-Yi Wu (National Cheng KungUniversity), Hong Kun Xu (National Sun YatsenUniversity), Jen-Chih Yao (National SunYat-sen University), Yuen Fong (NationalCheng Kung University), Mark C. Ho(National Sun Yat-sen University), Ying-FenLin (National Hualien University ofEducation), Jyh-Shyang Jeang (ROC MilitaryUniversity), Ruey-Lin Sheu (National ChengKung University), Chun-Hao Teng (NationalCheng Kung University), Chern-Shuh Wang(National Cheng Kung University), Mue-MingWong (Meiho Institute of Technology), Ngai-Ching Wong (National Sun Yat-senUniversity), and Tsai-Lien Wong (NationalSun Yat-sen University). There are also somepostdoctoral fellows actively participating intoour program: Bui Trong Kien (NSC, since2005), Kenji Kimura (NSC, since 2005), andD. R. Sahu (NSYSU, since 2007). Among all,the joining of Hong Kun Xu in 2006 is a veryimportant event. Xu is famous in functionalanalysis and nonlinear analysis. He is anelected member of the Academy of Science ofSouth Africa.Visiting Scientists(A) OptimizationXiaoqi Yang (Hong Kong PolytechnicUniv.), Duan Li (Chinese University of HongKong), Alex Rubinov (University of Ballarat),Louis Caccetta (Curtin University), ShengjieLi (College of Mathematics and Physics), JaneYe (Univ. of Victoria), David Gao (VirginiaPolytechnic Institute and State Univ.),Highlights of the Programs -›› 40

Hubertus Th. Jongen (Maastricht University),E. Polak (University of California atBerkeley), James R. Wilson (North CarolinaState Univ.), Xiaojiao Tong (ChangshaUniversity of Science and Technology), EricK.-W Chu (Monash University), Chen Ling(Zhejiang University of Finance andEconomics), S. Gustafson (University ofStavanger), J. J. Rückmann (Universidad delas Americas), O. Stein (University ofDuisburg-Essen), G. Still (University ofTwente).(B) AnalysisR. T. Rockafellar (Washington), W.Zelazko (Polish Academy), King-Fai Lai(Syndey), Zhi-Kin Wu (Alabama), G. G. Ding(Nankai), Chi-Kueng Ng (Nankai), Chi-WaiLeung (CU Hong Kong), Lu-Chuan Ceng(Shanghai Normal U.), Chi-Kwong Li(William and Mary), Nguyen Dong Yen(Vietnam Academy), Jim Jr. Douglas (Purdue),Nan-Jing Huang (Szechwan U.), Denny Lueng(Singapore), Xun-Hua Gong (Nanchang U.),Yakov Alber (Israel), Xie-Ping Ding(Szechwan Normal U.) and Genaro LopezAcedo (Seville). All of them offered eithershort courses or seminars on theirspecialization in functional analysis, operatoralgebras and theory, nonlinear analysis, andtheir applications. Especially, King-Fai Laiprovided us a month lone short course inJordan structures and Banach manifolds fromthe point of view of a number theorist. Thisgave us, and especially the students, a verysimulating experience.Frequent Visitors(A) OptimizationS-C Fang (North Carolina StateUniversity), K. L. Teo (Curtin University ofTechnology), Liqun Qi (Hong KongPolytechnic Univ.), M. Fukushima (KyotoUniversity), Macro Lopez (AlicanteUniversity), Shunsuke Hayashi (KyotoUniversity).(B) AnalysisAnthony To-Ming Lau (Alberta).Conferences and Workshops(A) Optimization• Conference on Sino-Japanese OptimizationMeeting (SJOM), Aug 27-30, 2008. Thismeeting will take place at NCTS, NationalCheng Kung University, Tainan, Taiwan.Organizers: M. Fukushima (KyotoUniversity), S. Y. Wu (National Cheng KungUniversity), Liqun Qi (Hong KongPolytechnic University) and J. C. Yao(National Sun Yat-Sen Univeristy). Plenaryspeakers: I. Ekeland (University of BritishColumbia), T. Y. Li (Michigan StateUniversity), A. Shapiro (Georgia Institute ofTechnology), J. Sun (National University ofSingapore), K. L. Teo (Curtin University ofTechnology), L. Qi (Hong Kong PolytechnicUniversity), M. Fukushima (KyotoUniversity), M. Kojima (Tokyo Institute ofTechnology), S. C. Fang (North CarolinaState University), S. Z. Zhang (The ChineseUniversity of Hong Kong), Y. X. Yuan(Chinese Academy of Sciences), Z. Q. Luo(University of Minnesota)• International Workshop on Semi-InfiniteProgramming, Aug 24-27, 2005 at NCTS,National Cheng Kung University.Organizers: S. Y. Wu (National Cheng KungUniversity), Marco Lopez (AlicanteUniversity), and Liqun Qi (Hong KongPolytechnic University). Plenary speakers: S.Gustafson (University of Stavanger), H. Th.Jongen (RWTH Aachen University), E.Polak (University of California at Berkeley),J. J. Rückmann (Universidad de lasAmericas), O. Stein (University of Duisburg-Essen), G. Still (University of Twente), K. L.Teo (Curtin University of Technology) and J.C. Yao (National Sun Yat-Sen University).• International Workshop on Optimization,May 17-20, 2004 at NCTS, National ChengKung University. Organizer: S. Y. Wu(National Cheng Kung University). Plenaryspeakers: A. M. Bagirov (University ofBallarat), L. Caccette (Curtin University ofTechnology), S-C Fang (North CarolinaState University), D. Li (The ChineseUniversity of Hong Kong), M. Mamedov(Suleyman Demirel University), L. Qi (Hong41‹‹- Highlights of the Programs

Kong Polytechnic University), A. Rubinov(University of Ballarat), K. L. Teo (CurtinUniversity of Technology), Y. H. Wu and X.Yang (Hong Kong Polytechnic University).(B) Analysis• In October and December 2005, we held twoworkshops in functional analysis andoperator theory. One of them was held atNational Dong Hwa University in Hualien.The theme of them emphasized onpromoting new research problems andencouraging fresh PhD's and graduatestudents to join the activities.• In December 25-28, 2004, we organized theNCTS Workshop in Functional Analysis atNSYSU and NCKU. The main speakerswere Liming Ge (New Hamspire, USA) andKa-Sing Lau (Hong Kong). Other speakersincluded Chi-Wai Leung (Hong Kong),Bingren Li (China), Jin Liang (China),Jinchuan Hou (China), G. G. Ding (China),Chi-Kueng Ng (China), Ti-Jun Xiao (China)and Ryotaro Sato (Okayama, Japan). Thepapers presented in the Workshop wereincluded in a special issue of Taiwanese J.Math. The Chinese colleagues were veryinterested in this activity. In 2005 and 2006,they continued the series in Chengdu byChinese Academy of Science, and inHuangshan by the Chinese University ofScience and Technology. Each of themattracted more than 300 participants, andsome of us were invited as the main guestsand steering committee members.• A biweekly seminar series on functionalanalysis was held in National Sun Yat-senUniversity in 2005 and 2006. Graduatestudents were invited to speak in theseminars. Postdoctoral fellows and youngresearchers were also welcome. Talks givenby Jyh-Shyang Jeang were on on localautomorphisms and local derivations onoperator algebras. Chin-Cheng Lin alsogave a talk on boundedness of theMarcinkiewicz integral.• In October 21-23, 2005, we held the 6 thTaiwan-Philippine Symposium on Analysisat NSYSU. About 20 Philippines analystsjoined us to explore in new advances invarious branches of analysis and itsapplications.• In April 3-7, 2006, we held the internationalWorkshop on Jordan Structures in Analysisand Geometry. This was an important eventin functional analysis and operator algebras.The list of invited speakers from aboardincluded C-H. Chu (London), C. M. Edwards(Oxford), Y. Friedman (Jerusalem), R.Iordanescu (Bucharest), J. M. Isidro(Santiago), W. Kaup (Tübingen), C. W.Leung (Hong Kong), M. Mackey (Dublin),M. Neal (Denison), C. K. Ng (China), T.Nomura (Kyushu), A. M. Peralta (Granada),L. Stacho (Szeged), H. Upmeier (Marburg),and B. Zalar (Maribor). There were also anumber of talks given by local analysts.Exchange Programs and InternationalCooperations(A) OptimizationProf. R. L. Sheu was invited by Prof. S. C.Fang to visit Department of IndustrialEngineering and Operations Research Programat North Carolina State University fromSeptember 25 to November 30, 2004. Prof. S.Y. Wu was invited by Prof. K. L. Teo to visitDepartment of Applied Mathematicas, HongKong Polytechnic University from November18 to November 21, 2004. Prof. S. Y. Wu wasinvited by Prof. Liqun Qi to visit Departmentof Applied Mathematics, Hong KongPolytechnic University from January 28 toFebruary 1, 2005 and April 13 to April 19,2006. Prof. S. Y. Wu was invited by Prof. JaneYe to visit Victoria University, Canada forresearch collaboration from May 13 to May22, 2005. Prof. C. S. Wang was an invited talkto attendant Sixth International Workshop onAccurate Solution of Eigenvalue Problems inU.S.A from May 20-27, 2006. Prof. S. Y. Wuwas an invited talk in Euro XXI OperationResearch Conference in Iceland from June 1-6,2006. Prof. R. L. Sheu was invited by Prof. S.C. Fang to visit Tsing Hua University atBeijing, China from June 1-6, 2006.Optimization Research group of NationalCenter of Theoretical Sciences have ancontract with the optimization center of HongKong polytechnic University withHighlights of the Programs -›› 42

collaboration research. Prof. S. Y. Wu wasinvited by Prof. E. Polak to visit Departmentof Electrical Engineering, Berkerly Universityin USA from March 11 to March 15, 2006 forresearch collaboration.Student's Seminars and Schools(A) OptimizationC. S. Wang: A biweekly seminar series onoptimal control: theory and computation washeld in NCTS, National Cheng KungUniversity in 2005 and 2006. Graduatestudents and young researchers were invited toattend the seminar.Part IIThe Accomplished and theAnticipations[1] Z. L. Wu and S. Y. Wu (2004), Weak SharpSolutions of Variational Inequalities inHilbert Spaces, SIAM Journal onOptimization, Vol. 14, 1011-1027.[2] S. J. Li, S. Y. Wu, X. Q. Yang and K. L.Teo (2006), A Relaxed Cutting PlaneMethod for Semi-Infinite Semi-definiteProgramming, Journal of Computationaland Applied Mathematics,Vol.196, 459-473.[3] Z. L. Wu and S. Y. Wu (2006),Characterizations of the Solution Sets ofConvex Programs and VariationalInequality Problems, Journal ofOptimization Theory andApplication,Vol.130, 341-360.[4] S. C. Fang, S. Y. Wu and S. I. Birbil,(2006) Solving Variational InequalitiesDefined on A Domain with InfinitelyMany Linear Constraints, ComputationalOptimization and Applications, Vol. 37,67-81.[5] L. C. Ceng and J. C. Yao (2007),Approximate proximal methods in vectoroptimization, European Journal ofOperational Research, to appear.[6] M. C. Ho and M. M. Wong (2006),Applications of the theory of s. n. functionsto the duality of analytic function spacesand the Hankel operators in $\mathcalS_\pi$, Indiana University Math. Journal,55, no. 5, 1646-1669.[7] Wen-Fong Ke, Bing-Ren Li and Ngai-Ching Wong (2004), Zero productpreserving maps of continuous operatorvalued functions, Proc. Amer. Math. Soc.,132, 1979-1985.[8] G. Marino and H.K. Xu (2007), Weak andstrong convergence theorems for strictpseudo-contractions in Hilbert Spaces, J.Math. Anal. Appl., 329, 336-346.[9] G. S. Wei, H.K. Xu, and Z.B. Xu, Leftdefinitespaces of singular Sturm-Liouvilleproblems, Journal of DifferentialEquations. (Accepted for publication inJanuary 2006.)[10] Ngai-Ching Wong, The triangle ofoperators, topologies and bornologies, inthe Proceedings of the 3rd InternationalCongress of Chinese Mathematicans,AMS-IP, to appear. (NSYSU)(A) OptimizationThe special issue for InternationalWorkshop on Semi-Infinite programming willbe published by Journal of Computational andApplied Mathematics in 2007. This specialissue contained 11 papers by internationalprofessors. In the direction of Infiniteprogramming, the exchange explicit methodwas developed by S. Y. Wu, have been made avery important algorithm for semi-infinite andinfinite programming problems. Theimplementation of the exchange explicitmethod for Infinite programming is verypowerful by compare it with the routine inMATLAB. For the infinite programming in L pspace and measure space, we have developedalgorithms for it. The implementation ofalgorithms is very well. Since manyalgorithms and theoretical work has been donein semi-infinite and infinite programming byS. Y. Wu, a research book in infiniteprogramming is prepared coauthors by S. Y.Wu, M. Lopez, and L. P. Zhang. The researchbook will published by Springer. This will bean important achievement in the area ofinfinite programming.43 ‹‹- Highlights of the Programs

(B) AnalysisIn operator algebras and function algebras,characterizing multiplicative maps amonglinear maps is a classical problem. In hisseminal paper, Kadison [1951, Ann. Math.]extended the classical Banach-Stone Theoremto show that every surjective isometry betweenC*-algebras is a Jordan isomorphism followedby a multiplication of unitary. Moreover, itsby-dual map is the sum of an automorphismand an antiautomorphism between W*-algebras. Ngai-Ching Wong extended this tothe non-surjective case in 2004, and to othercases including JB*-triples and variousfunction algebras subsequently. He is also aninvited 45-minute speaker in the ICCM2004.The paper [10] in the Proceedings ofICCM2004 concludes his 20 year works in thetheory of operator ideals on locally convexspaces starting from his 1988 paper publishedin Math. Ann.Mark C. Ho has been working on Hankeloperators for several years. The paper [6] issome new break through of him in this subject.Hong Kun Xu joined us in 2006. He haspublished many papers in functional analysis,fixed point theory and nonlinear analysis. Oneof his early papers was awarded by ISI as themost highly cited paper in Mathematics.Beside [8], the paper [9] is his attempt to applyhis technique to differential equations. Jen-Chih Yao is very productive recently andpublishes many papers a year. The paper [5] isone of them, which is sample of his elegance,and expected to be significant.Highlights of the Programs -›› 44

D.9 Partial Differential Equations at NCTS 2004-2007Coordinator: Jong-Shenq Guo (National Taiwan Normal University), Tai-Chia Lin (National Taiwan University)Chun-Kong Law (National Sun Yat-sen University), Chiun-Chuan Chen (National Taiwan University)Part I: Background and Activities inthe Programonlinear PDE at NCTS is a very broadfield. It covers not only theory ofdifferent types of PDE, but is also close relatedto applied sciences and other fields ofmathematics such as geometric analysis anddynamical systems. The activities in theprogram include regular PDE seminars,courses, workshops/conferences, andinternational cooperation.There have been more than 70 foreignvisitors and a lot of local people participatingin the PDE program since 2004. Many of thevisitors not only come forconferences/workshops, but also have joinedresearch projects with members of the localfocus group. For a report in this respect, seePart II.The PDE group in Taiwan has strongconnection with the PDE people in Japan andFrance. A few joint conferences with peoplemainly from these two countries have beenheld in recent years. We believe many othersimilar conferences and research projects willbe follow up continuously in the near future.Local Focus GroupJong-Shenq Guo (NTNU), I-Liang Chern(NTU), Chang-Shou Lin (NTU), Chiun-ChuanChen (NTU), Tai-Chia Lin (NTU), Jenn-NanWang (NTU), Chun-Chi Lin (NTNU), Huey-Er Lin (NTNU), Jenn-Long Chern (NCU), Je-Chiang Tsai (CCU), Sheng-Chen Fu (NCCU),Mao-Sheng Chang (Fujen U), Chung-TsunShieh (Tamkang U), Dong-Ho Tsai (NTHU),Chi-Kun Lin (NCTU), Chao-Nien Chen(NCUE), Chun-Kong Law (NSYSU)Visitors in 2004-2007Qing Han (University of Notre Dame),Yenheng Ding ( Academia Sinica, Beijing),Sergei Kuznetsov (University of Colorado atBoulder), Horng-Tzer Yau (HarvardUniversity), Mimura Masayasu (MeijiUniversity), Yisong Yang (PolytechnicUniversity), Peter Polacik (University ofMinnesota), Tai-Peng Tsai (University ofBritish Columbia), Xinfu Chen (University ofPittsburgh), Hongjun Yu (South ChinaUniversity of Technology), JiahongWu(Oklahoma State University), BoyanSirakov (The University of Paris 10), RenjunDuan (City University of Hong Kong), DavidKinderlehrer (USA), Eiji Yanagida (Japan),Ken-Ichi Nakamura (Josai University),Vladimir Sharafutdin (Russia), ToshikoOgiwara (Japan), Vladimir Zykov (Germany),Marek Fila (Slovakia), Hirokazu Ninomiya(Japan), Daishin Ueyama (Japan), Jame Sneyd(New Zealand), Noriko Mizoguchi (Japan),Peter Polacik (USA), Bei Hu(University ofNotre Dame), Dongho Chae (Korea), YuanLou (USA), Dimitrios Tzanetis (Greece),Nikos Kavallaris (Greece), Bernard Brighi(France), Hiroshi Matano (Japan), FrancoisHamel (University of Aix-MarseilleIII,France), Sun-Yung Alice Chang (PrincetonUniversity), Paul Yang (Princeton University),Gabriella Tarantello (Università di Roma TorVergata), Joel Spruck (Johns HopkinsUniversity), Bogdan Bojarski (PolishAcademy of Sciences), M. Chipot (Zurich,Swiss), Y. Giga (Tokyo, Japan), N. Kenmochi(Chiba, Japan), W.-M. Ni (Minneapolis, USA),M. Otani (Waseda, Japan), K. Sakamoto(Hiroshima U.), Z. Xin (Chinese U. of HongKong), Shih-Hsien Yu (City U. Hong Kong),Yoshitsugu Kabeya (Prefecture U), JyotshanaV. Prajapat (Fundamental Research), Der-ChenChang (Georgetown University), Ovidiu Calin45 ‹‹- Highlights of the Programs

(Eastern Michigan University), Augusto Ponce(University of Tours, France), Chun Liu (PennState University), Guofang Wang (Germany),Mu-Tao Wang (U of Columbia), Yung-SzeChoi (University of Connecticut), Tao Lu(Szechuen University), Min Mei (University ofConcordia), V. Pivovarchik (South-UkrainianState Pedgagogical Univerity), V.G. Romanov(Institute of Mathematics at Novosibirsk),Juncheng Wei (Chinese University of HongKong), V. Yurko (Saratov State University),Jun Zou (Chinese University of Hong Kong).Courses in 2004-2007• Topics in PDEs and Calculus ofVariations, March-June, 2007. Lecturer:Xiaofeng Ren (Utah State U). The courseaimed at the rigorous study of singularlyperturbed problems and variational problemswith non-locality. Models considered in thislecture included the Allen-Cahn problem inphase transition, the Cahn-Hilliard problemfor binary alloys, the Ginzburg-Landauproblem for superconductors, chargedLangumir monolayers, chiral liquid crystals,and most famously block copolymers.• Basic theory of ODEs and its applications,July-August, 2006, organized by Jong-ShenqGuo: This was a 6-week summer programfor senior undergraduate students. Studentsin any level are welcome to attend. Therewere about 15 students from sophomore toPh.D. program. Basic theory in ODE wasintroduced first and then some applicationsto special solutions (such as steady state,self-similar solution, traveling wave solution,etc.) of some PDE problems were given.• Summer Courses on PDE inMathematical Physics, July 10-31, 2006,organized by Yng-Ing Lee and Chiun-ChuanChen. This course covered two topics PDEand submanifolds in general relativity, givenby Mu-Tao Wang, and regularity problem forthe Navier-Stokes equations, given by Tai-Peng Tsai.• Mini-course on Stability estimates relatedto inverse problems for hyperbolicequations, April, 2006, organized by Chun-Kong Law. In the 6-hour minicourse,Vladmir Romanov (Institute of Mathematicsat Novosibirsk) discussed stability estimatesof one-dimensional and multi-dimensionalwave equations, as well as integral geometry(only two-dimensional case for simplicity).• A priori estimates in elliptic equations andrelated topics, July-August 2005, organizedby Jong-Shenq Guo and Chiun-Chuan Chen:This was a 6-week summer program forgraduate students. The first part covered themaximum principle, Schauder estimates,regularity theory of elliptic equations. Thispart was given by Jong-Shenq Guo, Sheng-Chen Fu and Je-Chiang Tsai. The secondpart, given by Tai-Chia Lin and Chiun-Chuan Chen, aimed at applications of theelliptic theory to several nonlinear equations• Mini-course in Nonlinear stability ofreaction diffusion equations, May, 2005,organized by Chi-Kun Lin. The 8-hour shortcourse was delivered by Ming Mei(Concordia University). It contains a detailedanalysis of the stability of traveling wavesolutions for a model of reaction diffusionequation with delay. This model came frombiology, the blowfly problem in Australia.• Mini-course in Dimension Analysis andDifferential Equations, April-May 2005,organized by Chun-Kong Law. This is a 12-hour short course delivered by Chi-Kun Lin(Cheng-Kung University) In this course theconcept of dimensional analysis wasintroduced and applied to study thedifferential equations. In particular, wefocussed on the Riesz potential, Hardy-Littlewood-Sobolev inequality, and therelated Sobolev type inequalities which areimportant in differential equations. Themethod of dimensional analysis was alsoused to give an intuitive idea about thefundamental solutions of the differentialequations.• Short Course on Integral Geometry,January 17-26, 2005, organized by Jenn-NanWang. Nine lectures were given by VladimirSharafutdin. The course started from theboundary rigidity problem: how far is aRiemannian metric on a compact manifoldwith boundary determined by distancesHighlights of the Programs -›› 46

etween boundary points? Afterlinearization, this gives the integral geometryproblem: to which extent is a symmetrictensor field on a Riemannian manifolddetermined by its integrals over geodesicsjoining boundary points? The latter questionis equivalent to an inverse problem for thekinetic equation on the unit tangent bundle.To treat the kinetic equation, some tensoranalysis machinery based on the structure ofthe tangent bundle was developed.Corresponding periodic integral geometryproblems for closed Riemannian manifoldswas discussed also. These problems areclosely related to the spectral rigidityproblem and need the technique of Anosovflows.• Mini-course Course in HamiltonianSytems and Its Quantization, January 31-February 3, 2005. Shao-Shiung Lin (NTU)gave three lectures. The contents included:(1) Newton's equations and the Hamiltonformulation, symmetry and the completeintegrability; (2) The KAM theory, and thetransition to chaos; (3) Quantization,Eninstein-Bohr-Summerfield quantizationconditions, and the quantum chaos. Thelectures were given in the morning and thestudents participated discussion sessions inthe afternoon.• Symmetry Methods and TheirApplications, September, 2004 - January,2005, organized by C.-P. Lo (ProvidenceUniversity). The lecturers were L. Wen(Peking U and Providence U), S.-S. Lin(NTU) C.-C. Chen (NTU), C.-P. Lo(Providence U). This course covered thetopics (1) Lie group (2) symmetry breakingin biological systems (3) moving planesmethod.• Mini-course in Harmonic Analysis and ItsApplications, April-June, 2004, organizedby Chi-Kun Lin. This 24-hour short coursewas composed of two topics: basic theory ofharmomic analysis and its application to theDirac-Klein-Gorden equations. The talkswere delivered by Chin-Cheng Lin (NationalCentral University) and Yung-Fu Fong(National Cheng Kung University). Theparticipants included related researchers andstudents in the Tainan-Kaohsiung area.Conferences and Workshops• NCTS 10 Years Anniversary Mini-Workshop on PDE July 23, 2007 at NTU.Organizers: Chiun-Chuan Chen and Tai-ChiaLin.• Speakers: Hung-Chi Kuo (Dept. ofAtmospheric Sciences, NTU), Chun-HsiungHsia (U. of Illinois at Chicago), Horng-TzerYau (Harvard U.)• Workshop on Reaction-Diffusion: Theoryand Applications December 1-2, 2006 atNTNU. Organizers: Jong-Shenq Guo andChiun-Chuan Chen.• Speakers: Masayasu Mimura (Meiji U.),Jong-Shenq Guo (National Taiwan NormalU.) Sze-Bi Hsu (National Tsing Hua U.)Shin-Ichiro Ei (Kyushu U.) YoshikazuTateishi (Kyushu U.) Yoshitsugu Kabeya(Perfecture U.) She-Feng Hsieh (NationalTaiwan Normal U.) Huey-Er Lin (NationalTaiwan Normal U.) Satoshi Sasayama(National Taiwan Normal U.) TatsuyukiNakaki (Hiroshima U.), Toshi Ogawa (OsakaU.), Li-Chang Hung (National Taiwan U.),Chiun-Chuan Chen (National Taiwan U.), Je-Chiang Tsai (National Chung Cheng U.),Yuzo Hosono (Kyoto Sangyo U.), Tai-ChiaLin (National Taiwan U.)• Workshop on Partial DifferentialEquations November 27, 2006 at NTU.Organizers: Chiun-Chuan Chen.• Speakers: David Kinderlehrer (CarnegieMellon University), Yoshitsugu Kabeya (Osaka Prefecture U), Jyotshana V. Prajapat(Tata Institute), Mitsuharu Otani ( WasedaU), Michel Chipot ( U of Zurich)• International Conference on NonlinearAnalysis November 20-25, 2006 at NCTS.• Organizing Committee: C.-C. Chen (Taipei,Taiwan), M. Chipot (Zurich, Swiss), P.G.Ciarlet (Hong Kong, China), J.-S. Guo(Taipei, Taiwan), N. Kenmochi (Chiba,Japan), C.-S. Lin (Chai-Yi, Taiwan), X. Pan(Shanghai, China), D.-H. Tsai (Hsinchu,Taiwan), Z. Xin (Hong Kong, China), E.Yanagida (Sendai, Japan)• Scientific Committee: Y. Giga (Tokyo,Japan), C.-S. Lin (Chai-Yi, Taiwan), W.-M.47 ‹‹- Highlights of the Programs

Ni (Minneapolis, USA)• Speakers: Bogdan Bojarski (Polish Academyof Sciences), Dong-Ho Chae (Korea), Jann-Long Chern (Jhongli, Taiwan), M. Chipot(Zurich, Swiss), P.G. Ciarlet (Hong Kong,China), Y. Giga (Tokyo, Japan), J.-S. Guo(Taipei, Taiwan), N. Kenmochi (Chiba,Japan), D. Kinderlehrer (Pittsburgh, USA),Tai-Chia Lin (Taipei, Taiwan), Tai-Ping Liu(Academia Sinica, Taiwan ), Y. Morita(Ryukoku, Japan), W.-M. Ni (Minneapolis,USA), M. Otani (Tokyo, Japan), M.Ramaswany (Bangalore, India), K.Sakamoto (Hiroshima, Japan), I. Shafrir(Haifa, Israel), S. Ukai (Hong Kong, China),J. Wei (Hong Kong, China), Z. Xin (HongKong, China), E. Yanagida (Sendai, Japan),Shih-Hsien Yu (Hong Kong, China), TatsukiKawakami (Tohoku U), Kota Ikeda (TohokuU) , Shota Sato (Tohoku U), YoshitsuguKabeya (Prefecture U), Jyotshana V. Prajapat(Fundamental Research), Makoto Narita(National Taiwan U), Yong-Hoon Lee (PusanNational U), Inbo Sim (Pusan National U),Tetsuya Ishiwata (Gifu U), KimieNakashima (Technology), Jongmin Han(Hankuk U of Foreign Studies), Jihoon Lee(Sungkyunkwan U), Akira Yanagiya(Waseda U), Yoshidazu Kobayashi (ChuoU), Noriaki Yamazaki (Muroran Institute ofTechnology), Ken Shirakawa (Kobe U),Toyohiko Aiki (Gifu U), Takesi Fukao (GifuNational College of Technology), YusukeMurase (Chiba U)• NCTS Workshop on Harmonic Analysisand Schrodinger Equations, July 11-12,2006 at NTU. Organizers: Chiun-ChuanChen and Horng-Tzer Yau.• Speakers: Horng-Tzer Yau (Harvard U.),Der-Chen Chang (Georgetown U.), Chi-KunLin (National Cheng Kung U.), Yung-FuFang (National Cheng Kung U.), Tai-PengTsai (U. of British Columbia), Ovidiu Calin(Eastern Michigan U.)• Workshop on Asymptotic AnalysisDecember 13, 2005 at NTNU. Organizer:Jong-Shenq Guo.• Speakers: Avner Friedman (MBI, Ohio StateU.), Jong-Shenq Guo (National TaiwanNormal U.), Minkyu Kwak (ChonnamNational U.), Noriko Mizoguchi (TokyoGakugei U.), Tai-Chia Lin (National TaiwanU.)• Prospects of Mathematical BiosciencesDecember 12-17, 2005 at NTNU. Organizer:Jong-Shenq Guo. Speakers: Avner Friedman(MBI, Ohio State U.)• Workshop on Nonlinear PDE and ParticleSystems July 5, 2005 at NTU. Organizers:Chiun-Chuan Chen. Speakers: Tai-Peng Tsai(U. of British Columbia), Horng-Tzer Yau(Stanford University).• Workshop in Inverse Problems April,2005 at NSYSU. Organizer: Chun-KongLaw. Speakers: Ming Jiang (Peking U.),Chin-Lung Lin (Chung-Cheng U.), Chun-Kong Law (Sun Yat-sen U.).• Workshop on Computer-Aided Analysisand Reaction-Diffusion SystemsSeptember 13-14, 2005 at NTNU. Organizer:Jong-Shenq Guo. Speakers: MasayasuMimura (Meiji U.), Daishin Ueyama(Hiroshima U.), Yoshio Yamada (WasedaU.), Mau-Hsiang Shih (National TaiwanNormal U.), Shih-Feng Shieh (NationalTsing Hua U.), Chiun-Chuan Chen (NationalTaiwan U.)• France-Taiwan Joint Conference onNonlinear PDEs and Related Topics July18-22, 2005 at NYU. Organizers: Chiun-Chuan Chen, Thierry Gallay, Jong-ShenqGuo (coordinator), Franc cois Hamel, Tai-Chia Lin and Lih-Chung Wang.• Speakers: Fabrice Bethuel (Universite ParisVI & IUF), Chiun-Chuan Chen (NationalTaiwan U.), Kuo-Chang Chen (NationalTsing Hua U.), Alain Chenciner (IMCCE &Universite Paris VII), Olivier Druet (EcoleNormale Superieure de Lyon), Maria J.Esteban (Universite Paris-Dauphine),Thierry Gallay (Universite Joseph FourierGrenoble I), Jong-Shenq Guo (NationalTaiwan Normal U.), Francois Hamel(Universite Paul Cezanne Aix-Marseille III),Cheng-Hsiung Hsu (National Central U.),Sze-Bi Hsu (National Tsing Hua U.), Chang-Shou Lin (National Chung Cheng U.), Chun-Chi Lin (National Taiwan Normal U.), Tai-Chia Lin (National Taiwan U.),Tai-Ping Liu(Academia Sinica, Taiwan), Yvan MartelHighlights of the Programs -›› 48

(Universite de Versailles-Saint-Quentin-en-Yvelines), Nikolai Nadirashvili (CNRS,LATP), Michel Pierre (ENS Cachan,Antenne de Bretagne), Jean-MichelRoquejoffre (Universite Paul SabatierToulouse III & IUF), Jean-Claude Saut(Universite Paris-Sud), Dong-Ho Tsai(National Tsing Hua U.), Je-Chiang Tsai(National Taiwan Ocean U.), Laurent Veron(Universite de Tours), Jenn-Nan Wang(National Taiwan U.), Frederic Weissler(Universite Paris 13)• Workshop on Reaction-DiffusionEquations and Related Topics May 26-31,2004 at NCTS. Organizers: Chang-Shou Lin,Eiji Yanagida and Chiun-Chuan Chen.• Speakers: Chao-Nien Chen (Changhua U. ofEducation), Chiun-Chuan Chen (NationalTaiwan U.), Jann-Long Chern (NationalCentral U.), Shin-Ichiro Ei (Kyushu U.),Jong-Shenq Guo (National Taiwan NormalU.), Qing Han (U. of Notre Dame), Sze-BiHsu (National Tsing Hua U.), KazuhiroIshige (Tohoku U.) Yoshitsugu Kabeya(Miyazaki U.), Chun-Kong Law (NationalSun Yat-sen U.), Chang-Shou Lin (NationalChung Cheng U.), Tai-Chia Lin (NationalChung Cheng U.), Yuki Naito (Kobe U.),Hirokazu Ninomiya (Ryukoku U.), ToshiOgawa (Osaka U.), Tetsutaro Shibata(Hiroshima U.), Yoshie Sugiyama (TsudaCollege), Izumi Takagi (Tohoku U.), ShingoTakeuchi (Kogakuin U.), MasaharuTaniguchi (Tokyo Institute of Technology),Dong-Ho Tsai (National Tsing Hua U.), EijiYanagida (Tohoku U.), Paul Yang (PrincetonU.), Yisong Yang (Polytechnic U.),ShojiYotsutani (Ryukoku U.)• International Conference on Elliptic andParabolic Problems - Recent AdvancesFebruary 16-20, 2004 at NCTS. Organizers:Chang-Shou Lin, Michel Chipot and Chiun-Chuan Chen.• Speakers: Herbert Amann (UniversitätZürich), Henri Berestycki (EHESS Paris),Fabrice Bethuel (Paris 6), Dongho Chae(Seoul National U.), Jann-Long Chern(National Central U.), Manuel Del Pino (U.of Chile), Pierpaolo Esposito (Roma TorVergata), Brice Franke (Ruhr UniversitaetBochum), Liliana Gratie (City U. of HongKong), Patrick Guidotti (U. of California atIrvine), Jong-Shenq Guo (National TaiwanNormal U.), Jongmin Han (Hankuk U. ofForeign Studies), David Kinderlehrer(Carnegie Mellon), Chun-Chi Lin (NationalTaiwan Normal U.), Tai-Chia Lin (NationalChung Cheng U.), Stephan Luckhaus(Universität Leipzig), Alessandra Lunardi(Università di Parma), Monica Musso(Politecnico di Torino) Frank Pacard (Paris12), Mariarosaria Padula (Università diFerrara), Jyotshana Prajapat (IndianStatistical Institute), Pavol Quittner(Comenius U.), José Francisco Rodrigues(U. of Lisbon), Pavel E. Sobolevskii(Hebrew U. of Jerusalem), VsevolodSolonnikov (Università di Ferrara), GabriellaTarantello (Roma Tor Vergata), Eiji Yanagida(Tohoku U.)Part II: The Accomplished and theAnticipationsSelected publications of the local focusgroup since 2004 :[1] Xinfu Chen and Jong-Shenq Guo, Selfsimilarsolutions of a 2-D multiple phasecurvature flow, Physica D, 229 (2007) 22-34.[2] Jong-Shenq Guo and Bei Hu, Blowup rateestimates for the heat equation with anonlinear gradient source term, to appear inDiscrete and Continuous DynamicalSystems.[3] Xinfu Chen, Jong-Shenq Guo, FrancoisHamel, Hirokazu Ninomiya, and Jean-Michel Roquejoffre, Traveling waves withparaboloid like interfaces for balancedbistable dynamics, Annales de l'InstitutHenri Poincar\'e - Analyse Non Lin\'eaire}24 (2007), 369-393.[4] S.M. Chang, C.S. Lin, T.C. Lin, W.W. Lin,Segregated nodal domains of twodimensionalmultispecies Bose-Einsteincondensates, Physica D 196(2004) no.3-4,pp. 341-361.[5] Tai-Chia Lin, Juncheng Wei, Spikes in two49 ‹‹- Highlights of the Programs

coupled nonlinear Schrodinger equations,Annales de L'institut Henri Poincare,Analyse non lineaire-nonlinear analysis, 22(2005) 403-439[6] Tai-Chia Lin, Juncheng Wei, Ground stateof N. coupled nonlinear Schrödingerequations in, R n ,n≤3, Comm. Math. Phys.255 (2005) 629-653.[7] Tai-Chia Lin, Juncheng Wei, Symbioticbright solitary wave solutions of couplednonlinear Schrödinger equations,Nonlinearity 19(2006)2755-2773.[8] Lin, Tai-Chia; Zhang, Ping Incompressibleand compressible limits of coupled systemsof nonlinear Schrödinger equations.Comm. Math. Phys. 266 (2006), no. 2,547-569[9] T.-L. Horng, S.-C. Gou, and T.-C. Lin,Bending-wave instability of a vortex ringin a trapped Bose-Einstein condensate,Phys. Rev. A 74, 041603(1-4) (2006)[10] Chen, C.-C., Lin, C.-S. and Wang, G.,Concentration phenomena of two-vortexsolutions in a Chern-Simons model., Ann.Sc. Norm. Super. Pisa Cl. Sci. (5) 3, no. 2(2004), 367-397[11] Bartolucci, Daniele, Chen, C.-C., Lin,Chang-Shou and Tarantello, Gabriella,Profile of blow-up solutions to mean fieldequations with singular data., Comm.Partial Differential Equations 29, no. 7-8(2004), 1241-1265.[12] Chen, C.-C., Chen, I-K., Liu, T.-P. andSone, Y., Thermal Transpiration forLinearized Boltzmann Equation, Comm.Pure Appl. Math 60, no 2 (2007), 147-163[13] Han, Qing; Hong, Jia-Xing; Lin, Chang-Shou On the Cauchy problem ofdegenerate hyperbolic equations. Trans.Amer. Math. Soc. 358 (2006), no. 9,4021-4044 (electronic).[14] Jost, J"urgen; Lin, Changshou; Wang,Guofang, Analytic aspects of the Todasystem. II. Bubbling behavior andexistence of solutions, Comm. Pure Appl.Math. 59 (2006), no. 4, 526-558[15] Chang-Shou Lin, Augusto C. Ponce,Yisong Yang, A system of ellipticequations arising in Chern-Simons fieldtheory, Journal of Functional Analysis247 (2007) 289-350.[16] Chang-Shou Lin, Pengfei Guan, GuofangWang, Local Gradient Estimates forQuotient Equations in ConformalGeometry, to appear in InternationalJournal of Mathematics (2007)[17] Mikko Salo and Jenn-Nan Wang,Complex spherical waves and inverseproblems in unbounded domains, InverseProblems, Vol 22 (2006), 2299-2309.[18] Horst Heck, Gunther Uhlmann, and Jenn-Nan Wang, Reconstruction of obstaclesimmersed in an incompressible fluid,Inverse Problems and Imaging, Vol. 1(2007), 63-76.[19] Gunther Uhlmann and Jenn-Nan Wang,Complex spherical waves for theelasticity system and probing ofinclusions, SIAM J. Math. Anal., Vol 38(2007), 1967-1980.[20] Ching-Lung Lin, Gen Nakamura, andJenn-Nan Wang, Three spheresinequalities for a two-dimensional ellipticsystem and its application, J. DifferentialEquations, Vol 232 (2007), 329-351.In [1], X. Chen and J.-S. Guo studied selfsimilarshrinking, stationary, and expandingsolutions of a two-dimensional motion bycurvature equation modeling evolution ofgrain boundaries in poly-crystals. Here theinterfacial energy densities were assumed todepend only on the grains and the Herringcondition was used for triple junctions (theintersections of three grain boundaries). Inparticular, in the isotropic case, a total of sixconfigurations were classified as the only selfsimilarshrinking solutions.In [2], J.-S. Guo and B. Hu studied aninitial boundary value problem for the heatequation with a nonlinear gradient sourceterm. It was shown that the blowup rate willnever match that of the self-similar variables.In the one space dimensional case withassumptions on the initial data so that theHighlights of the Programs -›› 50

solution is monotonically increasing in time,the exact blowup rate is found.In [3], X. Chen, J.-S. Guo, F. Hamel, H.Ninomiya, and Jean-Michel Roquejoffreconstructed cylindrically symmetric travelingwaves with paraboloid like interfaces forreaction-diffusion equations with balancedbistable nonlinearities. The main interest isabout solutions having interfaces that travelupwards in the vertical direction with aconstant speed. In particular, an answer to theDe Giorgi conjecture in parabolic version isgiven.The above three works are internationalcooperation under the support of NCTS, whichare acknowledged in these papers.Separation on systems of nonlinearSchrödinger equations (SNLS) (cf. [4]) is ajoint work of the focus group of NTU andNTHU. C.S.Lin and T.C.Lin (NTU) analyzedthe problem; S.M.Chang and W.W.Lin(NTHU) simulated the problem numerically.Spike solutions of coupled nonlinearSchrödinger equations (eg. [5]-[7]) is aninternational cooperation of Taipei andHongKong. Under the support of NCTS,T.C.Lin (NTU) and J.Wei (CUHK) havepublished a series of papers recently.Compressible and incompressible limitsof SNLS (cf. [8]) is an internationalcooperation of Taipei and Beijing. Due toNCTS supports, T.C.Lin (NTU) and P.Zhang(CAS) have more chance to work together.Bending-wave instability of Vortex ringdynamics in Bose-Einstein condensates (cf.[9]) is a cross-disciplinary work accomplishedby a domestic physicist (S.C.Gou) and twomathematicians. Such a work can be regardedas a successful cooperation of physicists andmathematicians in recent three years.Recently, a lot of work has been devoted toa Liouville type equation which arises fromprescribing curvature problem, Euler flows,Chern-Simon-Higgs model and chemotaxismodel. In two papers (published in CPAM,2003), C. C. Chen and C. S. Lin obtained aformula of the Leray-Schauder degree for thisequation. They continued their work toconsider degenerate case in [10] and singularsource case in [11].In [12], C. C. Chen, I. K. Chen, T. P. Liuand Y. Sone studied the flow of thermaltranspiration induced by the gradient of thewall temperature. This interesting flow cannotbe explained at the level of the Navier-Stokesequations. It has been known since the time ofMaxwell, but its mathematical formulation onthe basis of kinetic equations was done only inthe 1960s. They have constructed a steadystate flow of this phenomenon for thelinearized Boltzmann equation and beensuccessful to explain it at a rigorous level ofmathematics.In [15], C. S. Lin, A. C. Ponce, and Y. Yangproved the existence of topological vortices ina relativistic self-dual Abelian Chern-Simonstheory with two Higgs particles and two gaugefields through a study of a coupled system oftwo nonlinear elliptic equations over the entireplane.In [16], C. S. Lin, P. Guan and G. Wangextended the local gradient estimates to theconformal quotient equations. An existence ofsolutions of the conformal quotient equationsfollows from the local gradient estimates inthis paper and the paper of Gursky andViaclovsky.The stability of the inverse problem is animportant issue since most inverse problemsare notoriously ill-posed. A log type estimatewas already known for the inverseconductivity problem with full data. In [18], J.N. Wang with H. Heck and G. Uhlmannsuccessfully derived a log-log type estimatefor the inverse conductivity problem withpartial data.The theoretical aspect of the inverse nodalproblem is now well-studied. Uniqueness,reconstruction and stability issues are solved.X. Chen, Y.H. Cheng and C.K. Law try toapproximate the potential function with justone measurement of the nodal data. Theypropose three methods for the reconstruction,one of which is the Tikhonov regularizationmethod. All the three reconstructions inpreprint approximate the exact potential at anorder of 1/n.51 ‹‹- Highlights of the Programs

D.10 Probability Theory at NCTS 2004-2007Coordinator: Yuan-Chung Sheu (National Chiao Tung University)Part I: Background and Activities inthe Programhe wealth of complex genetic datafrom human and other genomeprojects has lead to the need for newprobability models to understand both thestructure of the data and the laws(if they exist)that govern biological systems. Also in thefinancial markets, the application ofprobability has revolutionized the industry. InNCTS, we focus on probability theory withapplications to finance and biology. We alsostudy convergence to equilibrium for ergodicMarkov processes. We report briefly ouractivities on probability theory during the pastfive years.Local Focus GroupBor-Sen,Chen (EE, NTHU), Guan-Yu Chen(NCTS, NCTU), Chuan-Hsiang Han (QF,NTHU), Wen-Ping Hsieh (IS, NTHU),Chung-Chin Lu (EE, NTHU), Henry Horng Shing Lu(IS, NCTU), Yuan-chung Sheu (AM, NCTU),WY Shu (IS, NTHU), Ching-Tang Wu(AM,NCTU)Short Term VisitorsCho-Jieh Chen (University of Alberta,Canada), Ren-Raw Chen (Rutger Busi-nessSchool,Rutger University), Jin-Chuan Duan(Rotman School of Management, University ofToronto, Canada), Chuan-HsiangHan(University of Minnesota and Ford MotorCo.), S.E.Kuznetsov (University of Colorado,USA), Wen-Hsiung Li(University of Chicago,USA), Alexander Schied (TechnicalUniversity Berlin, Germany)Symposium on Network BiologyThis symposium was token place on Friday,November 11, 2005. We aim to stimulate theinteraction of probability theory with biology,communication and related scientificapplications. There were about one hundredtwenty participants. Organizers: M.C.Huang(AC), C.C.Lu (NTHU), H.H.S.Lu (NCTU),Y.C.Sheu (NCTU), W.H.Lee (AC). Speakers:C.-H Yuh (National Health Research Institute),B.-S Chen (EE, NTHU), C.-P Hsu (Institute ofChemistry, Academia Sinica), W. V. Ng(Department of Biotechnology and LaboratoryScience in Medicine, National Yang MingUniversity), K.-L Ng (Department ofBiotechnology and Bioinformatics, AsiaUniversity), H.-C Huang (Institute ofBioinformatics, National Yang-MingUniversity), W.C. Liu (Institute of BiomedicalSciences, Academia Sinica), C. Y. Lin(National Health Research Institutes)Special Topics in 2004-2007• Credit Risk and Interest Rate Models(summer, 2005)• New mathematical challenges arising fromfinance include how to measure and controlrisk, how to model and hedge againstdefault, how to incorporate market frictions,and more generally, how to deal withimcomplete markets. We invited Jow-RenChan to give a short introductory course incredit risk. Also we invited Ren-Raw Chen,associate professor of Rutger BusinessSchool, Rutger University, to visit NCTS forone week. During his stay at NCTS,Professor Chen gave three lectures on hisresearch related to credit risk.• Cutoff Phenomenon for Markov Chains(summer, 2005)• The cut-off phenomenon (or thresholdHighlights of the Programs -›› 52

phenomenon) for finite state Markov chainswas first studied by Aldous and Diaconis. Itis wide-believed that this phenomenonshould be hold for most families of Markovchains. However it is rather difficult to verifythat a given family of chains satisfies thedefinition of cut-off phenomenon. We invitedGuan-Yu Chen to give a series of lectures onrecent progress on this interesting andchallenging subject.• Perturbation Methods in FinancialMathematics (spring, 2006)• Within the last decade, there have beenprogresses made to unveil the character-istic"smile" phenomenon in financial derivativesmarket. Professor Chuan-HsiangHan(Department of Quantitative Finance,NTHU) was the speaker of this special topic.Firstly, this short course introduces thecelebrated Black-Scholes formula and thesmile (or skew) effect in finance as aninverse problem. Then we utilize aperturbation method to tackle such problembased on some multiscale stochastic models.In addition, we discuss the Monte Carlopricing problem and its variance reductionby hedging portfolios in an incompletemarket.• Model Uncertainty, Robustness, and RiskMeasure (spring, 2006)• Professor Ching-Tang Wu gave a minicourseto introduce the probability theo-riesthat are needed in the financial mathematics.Topics include: Change of mea-sures, Utilitymaximization, Superhedging, Stochasticdifferential equations and their relation toPDE, Risk measures, Robust representationof convex risk mea-sures. Also ProfessorAlexander Schied (Department ofMathematics, Technische UniversitaetBerlin) gave a series of talks from March 23,2006 to April 23, 2006. Professor Schiedpresented several recent approaches fordealing with model risk. In particular, he alsohighlighted the use of convex risk measures.Another key topic was construction ofoptimal investment strategies under robustpreferences.Student's Seminars and Summer Courses• Student's Seminar on Probability Theory(2004)• We ran this regular seminar once a week.The main purpose of this seminar was toprovide a solid foundation on probability forthose who are interested in probability theoryand its applications. The main topics coveredare: characteristic functions, momentgeneratingfunctions, weak convergence,independence and convolution, weak law oflarge numbers, strong limit theorems, seriesof independent random variable, strong lawof large numbers, and central limit theorem.• Summer Course on Stochastic Processes(2004)• Markov chains and martingales are amongthe most basic mathematical models forrandom phenomena in both natural andsocial sciences. We gave ten lectures onthese two topics from early July toSeptember,2004. The topics covered were:conditional expectations, Markov chains,stopping times, countable state Markovchains, ergodic theorem, martingales,martingale convergence theorem, optionalstopping times, up-crossing inequality.• Student's Seminar on Stochastic Analysis(2005)• We run this regular seminar once a weekfrom August, 2005 to December, 2005. Themain purpose of this seminar was to providea solid foundation on stochastic analysis.The main topics covered are : stochasticintegration, infinitesimal generators,diffusions and Itô processes, linearcontinuous Markov processes.• Summer Course in Graphical models withBiological Applications (2005)• Graphical model is the combination of graphand probability theory. It has manyapplications in the complicated biologicalsystem. This course gives students the basicfoundation in this field and also introducesmany important method and applicationstoward analyzing the biological network.This course cover: graphs and hypergraphs,Conditional independence and Markov53 ‹‹- Highlights of the Programs

properties, Contingency tables, Multivariatenormal models, Models for mixed data.Lecturers includes: T.Y Huang, M. Fuchs,S.Y. Haung, Y.C. Sheu, C.C. Lu, J.N. Tseng,H.H.S. Lu, H.S. Huang, W.Y. Shu.• Summer Course on Probabilistic andStatistical Methods in Bioinformatics (2007)• Themes are: the analysis of one DNAsequence, the analysis of multiple DNA orprotein sequences, BLAST, gene expression,microarrays, evolutionary models,phylogenetic tree estimation. Lecturersinclude: C.C.Lee, W.P. Hsing, H.H.S. Lu,W.Y. Hsu, Y.H. Zhang. Two special lectureswere given by Wen-Hsiung Li and Bor-SenChen.Part II: The Accomplished and theAnticipations(Graphic Models) Graphical models bringtogether graph theory and probability theory ina powerful formalism for large-scalemultivariate modelling. While maintainingcontrol over the computational cost associatedwith these models, graphical models havebecome a focus of research in many appliedfields, including bioinformatics, informationtheory, signal and image processing. Themathematical structure of network/pathwayanalysis (which is one of the most challengingproblems in the era of functional genomics) isrelated to graphic models and theirprobabilistic properties. The theoreticproperties for reconstruction of regulatorynetworks have been explored by theperspectives of probability and statistics [9].We also investigated the regulatory networksof yeast as a model for eukaryotic cells [11,12] . These researches are conducted with thecollaborations with Dr. Wen-Hsiung Li at theUniversity of Chicago, Dr. Lei Li at theUniversity of South California, Dr. Huai-Kuang Tsai and others in Acdemia Sinica. Themain purpose of the paper [5] is to determinethe precise exon-ntron boundaries, i.e. thesplice sites, in the coding region od a gene. Adependency graph model is developed to fullycapture the intrinsic interdependency betweenbase positions in a splice site. Since theprediction of the splice sites in the codingregion of a gene is a crucial part in the genestructure prediction, it is believed that theresults of this paper will contribute to thedevelopment of an advanced program for theprediction of gene structure from the genomicDNA sequence.(Ergodic Markov Processes) Theconvergence question for ergodic Markovprocesses arises in many fields includingstatistical physics, computer science, biologyand more. In statistical physics, it is commonto have to estimate the average entropy of adynamical mechanism. In biology, thequestion could concern the position of the lastcommon ancestor of two related species in thehistory of evolution or the expected spatialstructure of a protein. The common problemposed by these questions is to estimate theaverage of a function with respect to aprobability measure . From the perspectiveof the Markov Chain Monte Carlo method, thisis achieved by simulating a Markov processwith limiting distribution and choos-ing thestate at a certain time T as a random sample.Mathematically, Markov processes areanalyzed in both qualitative and quantitativeaspects. Classical results on operator theoryare applicable to the qualitative study of theergodicity and the optimal convergence rate isclosely related to many constants, e.g. spectralgap, Sobolev constant and logarithmicSobolev constant. However, knowing thequalitative behavior is not sufficient tounderstand the mixing time, e.g. the randomtime T introduced above. In practice, variousheuristics are used to choose T.Logarithmic Sobolev constant. Thelogarithmic Sobolev inequality and the relatedconstant are introduced in the groundbreakingpaper of Gross. In his work, the entropy of aMarkov process was proved to convergeexponentially with rate the logarithmicSobolev constant. However, the computationof the logarithmic Sobolev constant is stilllimited to very simple cases. We obtained in[4] that the logarithmic Sobolev constant isexactly a half of its spectral gap for simplerandom walk on n-cycle, when n is even. Thisis the first nontrivial result in this direction.Highlights of the Programs -›› 54

Very different from the even case, Discanoisand Saloff-Coste computed out the case n=3and concluded that 2α 3

to analyze errors of hedging strategies whentrading a risky financial derivative. The centralproblem considered is to study some averagingeffect by means of singular and regularperturbation theory. It turns out this studyreveals an interesting implication in finance.Namely the key parameters of hedging errorsare dominated by very few factors though theoriginal pricing models can be complicated.On the current stage, C.H. Han hassuccessfully tested his theory by means ofMonte Carlo simulations. In the forthcomingresearch, C.H. Han plans to study thefollowing problems: 1. Provide a varianceanalysis to explain that some well-known butseparate developed variance reductionmethods are asymptotically the same underweak assumptions. 2. Develop efficient MonteCarlo methods to evaluate optimal stoppingproblems such as American options or gameoptions. These problems are typically relatedto some nonlinear martingale representations.3. Study the method of Quasi Monte Carlo bymeans of error analysis.References:[1] Guan-Yu Chen, Wai-Wai Liu, and LaurentSaloff-Coste. The logarithmic Sobolevconstant of some finite Markov chains.Annales de la Faculté des Sciences deToulouse, accepted, 2007.[2] Guan-Yu Chen and Laurent Saloff-Coste.The cutoff phenomenon for randomizedriffle shuffles.Random Structures andAlgorithms, accepted, 2007.[3] Guan-Yu Chen and Laurent Saloff-Coste.The cutoff phenomenon for ergodicMarkov processes. Submitted, 2007.[4] Guan-Yu Chen and Yuan-Chung Sheu. Onthe log-Sobolev constant for the simplerandom walk on the n-cycle: the evencases. J. Funct. Anal., 202(2):473-485,2003.[5] T.-M. Chen, C.-C. Lu, and W.-H. Li.Prediction of splice sites with dependencygraphs and their expanded Bayesiannetworks, Bioinformatics, vol. 21, no. 4,pp. 471-482, 2005.[6] Yu-Ting Chen, Cheng-Few Lee and Yuan-Chung Sheu. An ODE Approach for theExpected Discounted Penalty at Ruin inJump Diffusion Model, Finance andStochastics, vol. 11, no. 3, pp. 323-355,2007.[7] J.-P. Fouque and C.-H. Han. Evaluation ofCompound Options using PerturbationApproximation, Journal of ComputationalFinance, Vol.9/No. 1, 2005, pp. 41-61.[8] J.-P. Fouque and C.-H. Han. A MartingaleControl Variate Method for Option Pricingunder Stochastic Volatility Models,ESAIM: Probability and Statistics 11, 40-54, 2007.[9] L.M.,Li and H. H.-S., Lu. ExploreBiological Pathways from Noisy ArrayData by Directed Acyclic BooleanNetworks. Journal of ComputationalBiology, 12, 2, 170-185, 2005.[10] Alexander Schied and Ching-Tang Wu.Duality theory for optimal investmentsunder model uncertainty, Statistics andDecisions 23 (4), 199-217, 2005.[11] H.-K. Tsai, H. H.-S. Lu and W.-H. Li.Statistical methods for identifying yeastcell cycle transcription factors. PNAS(Proceedings of the National Academy ofSciences of the United States ofAmerica), 102, 38, 13532-13537, 2005.[12] H.-K. Tsai, G. T.-W. Huang, M.-Y. Chou,H. H.-S. Lu and W.-H. Li. Method foridentifying transcription factor bindingsites in yeast. Bioinformatics, 22, 14,1675-1681, 2006.Highlights of the Programs -›› 56

D.11 Scientific Computation at NCTS 2004-2007Coordinator: I-Liang Chern (National Taiwan University) and Wen-Wei Lin (National Tsing Hua University)omputational Science andEngineering now has become arapidly growing multidisciplinary researcharea in the scientific world. The rapid growthof high performance computers havetransformed the methodology of scientificinvestigation. Computing is nowaday joinedexperiment and theory as one of thefundamental tools of investigation. It is safeand cheap. Due to recent advances in softwareand hardware of computing technology,scientific computation is already regarded asan equal and indispensable partner, togetherwith the theoretical and experimental studiesin the pursuit of scientific knowledge andengineering design. In additional to promotinginterdisciplinary research activity with othersciences, the Scientific Computation programat NCTS also cooperates with other programsin Mathematics Division such as the PDE,Mathematical Biology, and DynamicalSystems programs. To stimulate such researchactivity, we conduct collaborative research thatinvolves international renowned scholars, localscientists, graduate students, and post-docs.We also provide timely short courses andseminars to bring the newest ideas to ourstudents and local researchers. Accordingly, inthe years 2004-2007, we have integratedresearchers from mathematics, physics andengineering. Regular joint seminars and shortcourses have been organized. We also heldinternational workshops on scientificcomputing to bring international researchesand local researchers together.Local Focus GroupNTU --- Chien-Cheng Chang, Chien LiuChang, Yu Ming Chang, I-Liang Chern, Ruey-Lin Chern, Ren-Wu Fang, Guang Yu Guo,Michitoshi Hayashi, M. J. Huang, J. H. Lee,Tony W. H. Sheu, Yu-Chen Shu, K. M. Shyue,Din Ping Tsai, W. Wang, D. L. Yang, J. Y.Yang; Fu-Jen --- C. C. Yen; NTOC --- S. F.Tsai; NTNU --- Wei-Chih Liu, T. M. Hwang,S. F. Shieh; NTOU --- Railing Chang, Hai-Pang Chiang; FEG --- Shen-Chung Chen;NCUE --- Shih-Hung Chen; NCHC --- Li-GanTien; LIT --- Yuan Fong Chau; NCU --- Pi-Gang Luan, S. Y. Yang; NCTU --- M. C. Lai,C. T. Wu, L. M. Yeh; NTHU --- W. W. Lin, W.C. Wang; Yuanpei University --- H. Y. Fan;NCCU --- Tai Huei Wei; NCKU --- Kuan-RenChen, Yung-Chiang Lan, C. S. Wang andNKU --- Y. C. Kuo. There are also 4 Ph.Dstudents in this group from NTHU.Post DoctorS. M. Chang (NTHU, 2003 - 2008), Y. C.Kuo (NCTS, 2004 - 2005), H. Y. Hu (NCTS,2004 - 2005) and Y. L. Huang (NTHU, 2004 -2008).VisitorsIn 2004, Eric K.-W. Chu (MonashUniversity), So-Hsiang Chou (Bowling GreenState University), Zhilin Li (North CarolinaState University), Musheng Wei (East ChinaNormal University, Shanghai), Biswa NathDatta (Northern Illinois University), ShufangXu (Peking University), Huaxiong Huang(Depart. of Math. and Statistics, YorkUniversity) and Qianshun Chang (The ChineseAcademy of Sciences) visited NCTS and gaveone or more speeches.In 2005, Ben-Yu Guo (Shanghai NormalUniversity) visited NCTS and taught oneNCTS & PU Joint Course - High-orderMethods for PDEs and Related Topics whichstarts in Spring term every Thursday atProvidence University. Professors Chi-TienLin (PU), Tsung-Min Hwang (NTNU) and57 ‹‹- Highlights of the Programs

Ming-Chih Lai (NCTU) were the organizers ofthis course. W. Hui (HK Science andTechnology), Richard Y-H Tsai (Univ. ofTaxes-Austin), S. Altschuler (Harvard Univ.)and L. Wu (Harvard Univ.) visited NCTS-Taipei.In 2006, Chern Shuh Wang (NCKU), So-Hsiang Chou (Bowling Green State University,USA), Eric Chu (Monash University,Australia), Zhaojun Bai (University ofCalifornia), Haw-ren Fang (University ofMaryland) and Dan'l Pierce (Director ofBusiness Development and Product MarketingCray Inc.) visited NCTS and gave one or morespeeches. Further, So-Hsiang Chou taught ashort course A Posteriori Estimation andAdaptive Methods. The subject of a posteriorierror estimation and adaptive methods forpartial differential equations is an exciting areain scientific computation. The purpose of thisshort course is to introduce some basic ideas inthe subject, assuming minimal knowledge inconvex analysis and numerical PDEs.Essential topics of error estimation andadaptive methods were covered in this course.He wrote an eighty-five page lecture note forthe course. Chiu-Yen Kao (Univ. ofMinnesota), Edward Jack (NCSU), WeizhuBao (National Univ. of Singapore), SauroSucci(National Research Council, Rome, Italy), Li-Tien Cheng, (University of California, SanDiego), Selim Esedoglu, (UniversityMichigan, Ann Arbor) and Richard Tsai(University of Texas, Austin) visited NCTS-Taipei.In 2007, Jian-Guo Liu (University ofMaryland), Roger Lee (University ofMaryland, College Park), LieJune Hsiao(University of Houston, USA), Eric Chu(Monash University, Australia) and So-HsiangChou (Bowling Green state University) visitedNCTS and gave one or more speeches.Furthermore, So-Hsiang Chou gave a shortcourse on Finite Element Methods andEigenvalue Problems from Jun. 21 to Jul. 24.The purpose of this course is to provide aforum for introducing some interestingresearch topics on eigenvalue problems. Theseinclude the computation of the steady solutionsarising from self-consistent Schrodinger-Poisson system, the quantum dot (interface)problems, the BEC problems that are ofcommon interest to a lot of local researchers.Shuyu Sun (Clemson University), ZhoweiShen (National Univ. of Singapore), RichardY-H Tsai (Univ. of Taxes - Austin) and Chiu-Yen Kao (Ohio State Univ.) visited NCTS-Taipei. In addition, Gene Golub (StanfordUniversity) will visit NCTS next Jan. 3 to Jan.10.Seminars, Short Courses and Workshops(1) Regular seminars (NCTS-Taipei):i. Biweekly seminar on scientificcomputing and Applied Mathematics(2004-2007).ii. Computation and Simulation MonthlySeminars on Nano-photonics (2004-2007).(2) NCTS Student's Seminar on ComputationalDynamical Systems: Jun. 28 - Sep. 6, 2004.The purpose of this seminar is to helpgraduate students understand the basics ofcomputational dynamical systems.Organizers are Wen-Wei Lin, Shih-FengShieh and Shu-Ming Chang (Dept. ofMath., NTHU).(3) NCTS 2005 Winter School on ScientificComputation: Jan. 17 - 27, 2005.(4) NCTS & PU Joint Course: High-orderMethods for PDEs and Related Topics,Spring term, 2005 (Every Thursday), Feb.24-Apr. 14, 2005, Providence University.This was a joint course and the courseconsists of four different topics which weretaught by different researchers. Inparticular, we invited Prof. Ben-Yu Guofrom Shanghai Normal University to talkabout Spectral Methods for PDEs. Prof.Guo is a well-known expert on SpectralMethods. The four topics are1. Finite difference methods forconservation laws, (Prof. Chi-Tien Lin,PU).2. Spectral methods for PDEs on boundedor unbounded domains, (Prof. Guo Ben-Highlights of the Programs -›› 58

Yu, Shanghai Normal University).3. Direct method for solving linear systemsfor general sparse linear systems, (Prof.Tsung-Min Hwang, NTNU).4. Introduction to incompressible flowcomputations, (Prof. Ming-Chih Lai,NCTU).(5) An Introduction to Surface Plasmon I, II,III Apr. 2005, by Ruei-Lin Chern (AppliedMechanics, NTU).The aim is to give a brief introduction ofsurface plasmon problems tomathematicians.(6) Lagrangian-Type Computational FluidDynamics, May-June, 2005, by Prof. Hui(HKST).This two-month course provides a thoroughstudy on the Lagrange-type method andunified Euler and Lagrange method forcompressible Euler equations.(7) International Symposium on DynamicalSystem and Numerical Analysis in honorof Tien-Yien Li's 60th Birthday, May 10-12, 2005.(8) NCTS Seminar on Scientific Computation2006: Jan. 20-25, 2006.(9) Lattice Boltzmann Methods: Basic Theoryand Selected Applications I-IV, Feb. 2006,by SauroSucci (National Research Council,Rome, Italy).The course is based on the lecturer's newbook on Lattice Boltzmann Method.(10) A Short Course 2006 on a PosterioriEstimation and Adaptive Methods: May 17- Jun. 15, 2006.The purpose of this short course is tointroduce some basic ideas in the subject,assuming minimal knowledge in convexanalysis and numerical PDEs. The maintopics covered are as follows.1. Finite Element, Finite Difference, andFinite Volume Methods.2. Posteriori Error Estimation.3. Design of Adaptive Methods for SolvingSource and Eigenvalue Problems.(11) International Workshop on ScientificComputing (Tutorial Week): Jun. 15-23,2006.In the summer break of 2006, we organizeda short course on Scientific Computationthat lasted three days. There were fivelectures which covered different topics ofnumerical analysis and methods: Numericalapproximations of high frequency wavepropagation, Inverse problems, Level setmethods, Tsitsiklis' algorithms for solvingeikonal equations, and Image processing.Day 1: Tutorial 1. Mathematical modelsand numerical methods for highfrequencywaves (Prof. OlofRunborg, KTH, Sweden).Day 1: Tutorial 2. Inverse ProblemsInvolving Shapes (Prof. Chiu-YenKao, University of Minnesota).Day 2: Tutorial 3. Local Level Set Methods(Prof. Li-Tien Cheng, University ofCalifornia, San Diego).Day 2: Tutorial 4. Fast Algorithms forSolving Static Hamilton-JacobiEquations (Prof. Richard Tsai,University of Texas, Austin).Day 3: Tutorial 5. Level Set and DiffuseInterface Models in ImageProcessing (Prof. Selim Esedoglu,University Michigan, Ann Arbor).(12) International Workshop on ScientificComputing: Jun. 26 - 30, 2006.There has been significant progress inscientific computing, particularly in thediverse fields of multiscale computationsand imaging. One of the focuses ofmultiscale computation concentrates onproblems where classical single physicsmodels are either inadequate or notaccurate enough, and a coupling of multiplephysics models needs to be considered. Inparticular, there is an emergence ofmethods that replace heuristics andempirical observations in coarse scalesingle physics models by direct numericalsimulations of more accurate models59 ‹‹- Highlights of the Programs

defined on finer scales. PDE-basedtechniques for imaging received a lot ofattention due to its success in removingnoise and segmenting salient features inimages. Many of the approaches are closelyrelated to inverse problems and interfaceproblems. This workshop brings some ofthe world's leading experts in these fieldstogether and aims at (1) providing anopportunity for direct communication andexchange of ideas; (2) promotinginteraction and collaboration of local andinternational scholars. The workshopincluded 35 invited speakers and totalnumber of participant is 120 roughly.(13) School on Modern Numerical Methods inMath and Physics: Jul. 3 - 5, 2006.In recognizing this trend, NCTS sponsoreda school on modern numerical methods andalgorithms in math and physics forinterested graduate students and novices inthe field. The topics include large scalematrix computation, Monte Carlo method,Bayesian approach in curve fitting,numerical gravity, and GRID computing.The workshop included eight plenaryspeakers (Masayuki Asakawa, Ying Chen,Anthony Kennedy, Simon Lin, Chuan Liu,Jian-Guo Liu, Wai-Mo Suen and ChaoYang). They are world-known in theseareas of Applied Mathematics and the totalnumber of participant is 85 roughly.(14) Nanoplasmonics: Optical Properties ofPlasmonic Nanosystems, Winter 2006.This short course is given by NikolayZheludev. The content of this courseinclude a broad introduction to the topic ofplasmonic nanophotonics. It's aim is todiscuss how fundamental causality, i.e., theimpossibility to change the past, definespossible and impossible in optics andnanoplasmonics.(15) Coherent, Nonlinear and UltrafastNanoplasmonics, Winter 2006.This short course is given by MarkStockman. This course covers: (1) Problemof nanoscale control of local optical fields.(2) Coherent control using phase (temporal)degrees of freedom of ultrashort pulse inlinear and nonlinear processes. (3) Twopulse(interferometric) coherent control -full suppression or enhancement of nearfield hot spots for two-photon effects. (4)Surface plasmon amplification bystimulated emission of radiation (SPASER).(16) Discontinuous Galerkin Methods forFlow and Transport Problems I-IV, Jan.2007, by Shuyu Sun (Clemson University).This short course gives an introduction ofthe discontinuous Galerkin method and itsapplications.(17) A Short Course 2007 on Finite ElementMethods and Eigenvalue Problems: Jun.21-Jul. 24, 2007.(18) Nanophoto Nanophotonic BandgapStructures and Optical Microsystems,Spring 2007.This short course is given by Ai Qun Liu.The aim of this course is to introduce thefundamental theory, fabrication process andapplications of plasmonic bandgapstructures.In addition, a workshop Recent Advancesin Numerical Methods for EigenvalueProblems (RANMEP2008) will be taken placebetween Jan. 4-8, 2008.Selected Publications of the Local FocusGroup since 2004Martix analysis and computation(Inverse Quadratic Eigenvalue Problems)Given k pairs of complex numbers and vectors(closed under conjugation), we consider theinverse quadratic eigenvalue problem ofconstructing nxn real symmetric matrices M,C, and K (with M positive definite) so that thequadratic pencil has the given k pairs aseigenpairs. Using various matrixdecompositions, we first construct a generalsolution to this problem with k is lower orequal to n. Then, with appropriate choices ofdegrees of freedom in the general solution, weconstruct several particular solutions withadditional eigeninformation or specialproperties [1,13,15].Highlights of the Programs -›› 60

In [2], we propose a minimax scalingprocedure for second order polynomialmatrices that aims to minimize the backwarderrors incurred in solving a particularlinearized generalized eigenvalue problem.We consider the regularization problem forthe linear time-varying discrete-time periodicdescriptor systems by derivative andproportional state feedback controls. Sufficientconditions are given under which derivativeand proportional state feedback controls can beconstructed so that the periodic closed-loopsystems are regular and of index at most one.The construction procedures used to establishthe theory are based on orthogonal andelementary matrix transformations and can,therefore, be developed to a numericallyefficient algorithm. The problem of finite poleassignment of periodic descriptor systems isalso studied [4].Numerical methods and simulation in PDEIn [3], the work investigates the existenceof monotonic traveling wave and standingwave solutions of RTD-based cellular neuralnetworks in the one-dimensional integer latticeZ1. For nonzero wave speed c, applying themonotone iteration method with the aid of realroots of the corresponding characteristicfunction of the profile equation, we canpartition the parameter space ( , )-planeinto four regions such that all the admissiblemonotonic traveling wave solutionsconnecting two neighboring equilibria can beclassified completely.We extend our previous work (M.-C. Laiand W.-C. Wang, Numer Methods PartialDifferential Eq., 18:56-68, 2002) fordeveloping some fast Poisson solvers on 2Dpolar and spherical geometries to an ellipticaldomain. Instead of solving the equation in anirregular Cartesian geometry, we formulate theequation in elliptical coordinates. The solverrelies on representing the solution as atruncated Fourier series, then solving thedifferential equations of Fourier coefficientsby finite difference discretizations. Using agrid by shifting half mesh away from the poleand incorporating the derived numericalboundary value, the difficulty of coordinatesingularity can be elevated easily [5].In [6], we propose a simple finite differencescheme for the elliptic interface problem witha discontinuous diffusion coefficient using abody-fitted curvilinear coordinate system. Theresulting matrix is symmetric and positivedefinite. Standard techniques of accelerationsuch as PCG and multigrid can be used toinvert the matrix. The main advantage of thescheme is its simplicity: the entries of thematrix are simply the centered differencesecond order approximation of the metrictensor. In particular [10], a fast direct solverderived from the equation and the semicoarseningmultigrid are shown to be almostscalable with the problem size and outperformother preconditioners significantly.We propose two iterative methods, aJacobi-type iteration and a Gauss-Seidel-typeiteration (GSI), for the computation of energystates of the time-independent vector Gross-Pitaevskii equation (VGPE) which describes amulti-component Bose-Einstein condensate(BEC). A discretization of the VGPE leads toa nonlinear algebraic eigenvalue problem(NAEP). We prove that the GSI methodconverges locally and linearly to a solution ofthe NAEP if and only if the associatedminimized energy functional problem has astrictly local minimum. The GSI method canthus be used to compute ground states andpositive bound states, as well as thecorresponding energies of a multi-componentBEC [7,8,9]. On the other hand, we presenttwo efficient and spectrally accurate numericalmethods for computing the ground and firstexcited states in Bose-Einstein condensates[12].In [11], we present an asymmetricwatermarking method for copyright protectionthat uses different matrix operations to embedand extract a watermark. It allows for thepublic release of all information, except thesecret key. We investigate the conditions for ahigh detection probability, a low false positiveprobability, and the possibility of unauthorizedusers successfully hacking into our system.The robustness of our method is demonstratedby the simulation of various attacks.61 ‹‹- Highlights of the Programs

We describe an integral equation approachfor simulating diffusion problems with movinginterfaces. The solutions are represented asmoving layer potentials where the unknownsare only defined on the interfaces. Theresulting integro-differential equation systemis solved using spectral deferred correctiontechniques developed for general differentialalgebraic equations, and the time dependentpotentials are evaluated efficiently using fastconvolution algorithms [14].In [16], we give an error estimate for theenergy and helicity preserving scheme (EHPS)in second order finite difference setting onaxisymmetric incompressible flows withswirling velocity. This is accomplished by aweighted energy estimate, along with carefuland nonstandard local truncation error analysisnear the geometric singularity and a far fielddecay estimate for the stream function. A keyingredient in our a priori estimate is thepermutation identities associated with theJacobians, which are also a unique feature thatdistinguishes EHPS from standard finitedifference schemes.We present a simple volume-of-fluidapproach to interface tracking for inviscidcompressible multicomponent flow problemsin two space dimensions. The algorithm uses auniform Cartesian grid with some grid cellssubdivided by tracked interfaces,approximately aligned with the materialinterfaces in the flow field. A standardvolume-moving procedure consists of twobasic steps. We validate our algorithm byperforming the simulation of a Mach 1.22shock wave in air over a circular R22 gasbubble, where sensible agreement of some keyflow features of the computed solutions areobserved when direct comparison of ourresults are made with the existing experimentaland numerical ones that appear in the literature[17].In [18], the discrete convection-diffusionequations obtained from streamline diffusionfinite element discretization are solved on bothuniform meshes and adaptive meshes.Estimates of error reduction rates for bothgeometric multigrid (GMG) and algebraicmultigrid (AMG) are established on uniformrectangular meshes for a model problem. Ouranalysis shows that GMG with line Gauss-Seidel smoothing and bilinear interpolationconverges, and AMG with the same smootherconverges more rapidly than GMG.At the heterogeneity scale the flow isdescribed by a two-phase flow model with ageneralized Darcy law, classical phasepermeabilities and capillary pressure. Themacroscale flow model is obtained by the twoscaleasymptotic homogenization method. Tosolve the cell problems we have developed thetwo-phase version [19].In [20], we devoted to analyze a splittingmethod for solving incompressible inviscidrotational flows. The problem is first recastinto theve locity-vorticity-pressure formulationby introducing the additional vorticityvariable, and then split into three consecutivesubsystems.[1] M. T. Chu, Y. C. Kuo, and W. W. Lin, OnInverse Quadratic Eigenvalue Problemswith Partially Prescribed Eigenstructure,SIAM Matrix Anal. Appl., Vol. 25, No. 4(2004), 995-1020.[2] H. Y. Fan, W. W. Lin, and P. Van Dooren,Normwise Scaling of Second OrderPolynomial Matrices, SIAM Matrix Anal.Appl., Vol. 26, No. 1 (2004), 252-256.[3] C. H. Hsu and Suh-Yuh Yang, Wavepropagation in RTD-based cellular neuralnetworks, J. Differential Equations, 204(2004), pp. 339-379.[4] Y. C. Kuo, W. W. Lin, and S. F. Xu,Regularization of Singular LinearDiscrete-Time Periodic Systems byDerivative and Proportional StateFeedback, SIAM Matrix Anal. Appl., Vol.25, No. 4 (2004), 1046-1073.[5] Ming-Chih Lai, Fast direct solver forPoisson equation in a 2D elliptical domain,Numer. Methods Partial DifferentialEquations 20 (2004), no. 1, 72-81.[6] Wei-Cheng Wang, A jump conditioncapturing finite difference scheme forelliptic interface problems, SIAM J. Sci.Highlights of the Programs -›› 62

Comput. 25 (2004), no. 5, 1479-1496.[7] S. M. Chang, W. W. Lin, and S. F. Shieh,Gauss-Seidel-type Methods for EnergyStates of a Multi-Component Bose-EinsteinCondensate, J. Comp. Physics, Vol. 202,Issue 1 (2005), 367-390.[8] Tsung-Min Hwang and Weichung Wang,Energy States of Vertically AlignedQuantum Dot Array with NonparabolicEffective Mass, Computers andMathematics with Applications, 49:39-51,(2005).[9] Y. C. Kuo, W. W. Lin, and S. F. Shieh,Bifurcation Analysis of a Two-ComponentBose-Einstein condensate, Physica D, Vol.211, No. 3-4 (2005), 311-346.[10] Ming-Chih Lai and Yu-Hou Tseng, A fastiterative solver for the variable coefficientdiffusion equation on a disk, J. Comput.Phys. 208 (2005), no. 1, 196-205.[11] Jengnan Tzeng, Wen-Liang Hwang, and I-Liang Chern, An asymmetric subspacewatermarking method for copyrightprotection, IEEE Trans. Signal Process.53 (2005), no. 2, part 2, 784-792.[12] Weizhu Bao, I-Liang Chern, and FongYin Lim, Efficient and spectrally accuratenumerical methods for computing groundand first excited states in Bose-Einsteincondensates, J. Comput. Phys. 219(2006), no. 2, 836-854.[13] J. Carvalho, B. N. Datta, W. W. Lin, andC. S. Wang, Symmetric PreservingEigenvalue Embedding in Finite ElementModel Updating of Vibrating Structures,J. Sound and Vibration, Vol. 290(3-5)(2006), 839-864.[14] Jingfang Huang, Ming-Chih Lai, andYang Xiang, An integral equation methodfor epitaxial step-flow growthsimulations, J. Comput. Phys. 216 (2006),no. 2, 724-743.[15] Y. C. Kuo, W. W. Lin and S. F. Xu,Solutions of the Partially DescribedInverse Quadratic Eigenvalue Problem,SIAM Matrix Anal. Appl., Vol. 29, No. 1(2006), 33-53.[16] Jian-Guo Liu and Wei-Cheng Wang,Convergence analysis of the energy andhelicity preserving scheme foraxisymmetric flows, SIAM J. Numer.Anal. 44 (2006), no. 6, 2456-2480.[17] Keh-Ming Shyue, A wave-propagationbased volume tracking method forcompressible multicomponent flow in twospace dimensions, J. Comput. Phys. 215(2006), no. 1, 219-244.[18] Chin-Tien Wu and Howard C. Elman,Analysis and comparison of geometricand algebraic multigrid for convectiondiffusionequations, SIAM J. Sci.Comput. 28 (2006), no. 6, 2208-2228.[19] Li-Ming Yeh, Homogenization of twophaseflow in fractured media, Math.Models Methods Appl. Sci. 16 (2006), no.10, 1627-1651.[20] Chiung-Chiou Tsai and Suh-Yuh Yang,Analysis of a splitting method forincompressible inviscid rotational flowproblems, J. Comput. Appl. Math. 200(2007), no. 1, 364-376.The development of computational scienceneeds integration of researchers from differentdisciplines: mathematics, physics, chemistry,biology, geoscience, engineering, computerscience, etc. The funding of NCTS-Taipeiprovided opportunities to bring researchersfrom different disciplines together. In thisthree-year period, we focus on threeinterdisciplinary topics: (1) core algorithms,(2) computational fluid dynamics, and (3)computational nano-optics.Core algorithmCore algorithm focuses on interfaceproblems, multigrid methods, numericalmethods for nanoscale transport based onquantum kinetic theory, fast iterative solversfor unsymmetrical and indefinite large-sizematrix equations [11, 25, 26, 27, 31].Computational fluid dynamicsComputational fluid dynamics focuese onCFD code implementation on PC-cluster,multi-grid and multi-level, preconditioner63 ‹‹- Highlights of the Programs

designs for flow solver. Application of CFDtechnique to computational medicine andindustrial problems [23, 24, 25, 28, 29].Nano-optics focusesNano-optics focuses on investigating thetopics of optical responses in nanometer scaleand the resultant intriguing phenomena such assurface plasmon resonances, plasmonic bandgaps, and anomalous light propagation inmeta-materials [21, 22, 30, 32].[21] S. C. Chen, D. P. Tsai, NumericallyInvestigating Near-field Scattering forSpatial Enhancement of Single IrregularNano Plasma particle, Scanning 26 (5),109-112, (2004).[22] R. T. Hong, M. J. Huang and Jaw-YenYang, Molecular dynamics study ofcopper trench filling in damasceneprocess, Materials Science inSemiconductor Processing, 8, pp. 587-601, (2005).[23] Tony W. H. Sheu, C. W. Chou, Eric S. F.Tsai, P. C. Liang, Three-dimensionalanalysis for radio-frequency ablation ofliver tumor with blood perfusion effect,Computer Methods in Biomechanics andBiomedical Engineering, Vol. 8(4) (2005),pp. 229-240[24] R. K. Lin, Tony W. H. Sheu, Applicationof dispersion-relation-preserving theoryto develop a two-dimensional convectiondiffusionscheme, Journal ofComputational Physics, Vol. 208 (2005),pp. 493-526.[25] P. H. Chiu, Tony W. H. Sheu, R. K. Lin,Development of a dispersion-relationpreservingupwinding scheme forincompressible Navier-Stokes equationson non-staggered grids, Numerical HeatTransfer. Part B: Fundamentals, Vol.48(6) (2005), pp. 543-569.[26] Tony W. H. Sheu, R. K. Lin, Developmentof locally analytic prolongation operatorin two-grid three-level method forincompressible Navier-Stokes equations,Numerical Heat Transfer. Part B:Fundamentals, Vol. 50(6) (2006), pp. 517-533.[27] R. K. Lin, Tony W. H. Sheu, Developmentof a class of multiple time-steppingscheme for convection-diffusion equationsin two dimensions,International Journalfor Numerical Methods in Fluids, Vol.52(12) (2006), pp. 1293-1313.[28] H. P. Rani, Tony W. H. Sheu, T. M.Chang, P. C. Liang, Numericalinvestigation on non-Newtonianmicrocirculatory blood flow in hepaticlobule, Journal of Biomechanics, Vol. 39(2006), pp. 551-563.[29] Yang, J. Y., T. Y. Hsieh and Y. H. Shi, AKinetic Flux Vector Splitting Scheme forIdeal Quantum Gas Dynamics, SIAM J.on Scientific Computing, Vol. 29, No. 1,pp. 221-244 (2007).[30] Y. H. Shi, J. C. Huang and Jaw-Yen Yang,High Resolution Kinetic Beam Schemes inGeneralized Coordinates for IdealQuantum Gas Dynamics, J. Comput.Phys., Vol. 222, pp. 573-591 (2007).[31] Chern, I-Liang and Yu-Chen Shu,Coupling interface method for ellipticinterface problems, Journal ofComputational Physics, no. 225 (2007),2138-2174.[32] Tony. W. H. Sheu, Y. H. Chen, Numericalstudy of flow field induced by alocomotive fish in the moving meshes,International Journal for NumericalMethods in Engineering, Vol. 69 (2007),pp. 2247-2263.Highlights of the Programs -›› 64

Activities of Onsite ScientistsTitleNameFieldPeriodJiun-Cheng ChenAlgebraic Geometry2006/09/01-2007/08/31Wen-Ching Winnie LiNumber Theory2006/09/01-2007/08/31Song-Sun LinDynamical Systems2004/08/01-2008/12/31Center ScientistsWen-Wei LinScientific Computation2006/09/01-2007/08/31Dong-Ho TsaiPartial Differential Equations2006/09/01-2007/08/31Chin-Lung WangAlgebraic Geometry2004/01/01-2008/12/31Jing YuNumber Theory2004/01/01-2008/12/31Visiting ProfessorVisiting AssistantProfessorDer-Chen ChangGuan-Yu ChenGeometric AnalysisProbabilityStochastic Processes2007/05/23-2007/08/232006/12/23-2007/03/232006/08/01-2007/07/31PostdoctoralFellowYan-Hsiou ChengChian-Jen WangYou-Chiang YiDynamical SystemsNumber TheoryNumber Theory2007/03/01-2008/02/292006/08/01-2007/07/312006/08/01-2007/07/31.1 Center ScientistsI. Jiun-Cheng ChenNational Tsing-Hua University,Assistant ProfessorConferences and visiting-France-An algebraic geometry conference, IHP, Paris-Korea-Algebraic geometry seminar, KIAS, SeoulKorea-Japan-Algebraic geometry seminar, RIMS, Kyoto,Japan-Hong Kong-Geometry seminar, Chinese Hong KongUniversity, Hong Kong-Taiwan-TIMS Conference on Higher dimensionalGeometry, TIMS, Taipei, TaiwanNCTS ActivitiesOrganizer, Workshop on the minimal modelprogram, NCTS, Hsinchu, TaiwanResearch Works(joint with H. H. Tseng) A note on derivedMcKay correspondence, mathAG0609737,submitted to MRL65 ‹‹- Activities of onsite Scientists

II. Wen-Ching Winnie LiPennsylvania State UniversityNational Center for Theoretical Sciences,Center ScientistTeaching• Advanced graduate course on ModularForms and Galois Representations, fall 2006,NCTS• Reading course on Arithmetic of EllipticCurves, with Ms. Pei-Yu Tsai, a junior atNational Taiwan University, spring andsummer 2007Conferences-Taiwan-• Taiwanese Mathematical Society AnnualMeeting, Dec. 2006, Taipei• Plenary address "A century of modularforms"• International Conference on GaloisRepresentations and Function FieldArithmetic, May 2007, organizer-Canada-• International Conference on Polynomialsover Finite Fields and Applications, BanffInternational Research Station, Banff,November 2006• Invited speaker, "Characterizations ofpseudo-codewords of parity-check codes"-China-• The 1st Workshop on Number Theory,Combinatorics and their Interactions, August2007, Nanjing• Invited plenary speaker, "Zeta functions ofgraphs and complexes"• International Conference on Algebra andRelated Topics in honor of ProfessorZhexian Wan's 80th birthday, August 2007,Beijing• Invited speaker, "Pseudo-codewords oflow-density parity-check codes"November 2006, invited participant• Workshop on Expanders and Nano-scaleSelf-assembly, Hewlett Packard Lab, PaloAlto, CA, November 2006, organizer• Invited speaker, "Ramanujan graphs andhypergraphs"• International FNANO 2007 Conference,Snowbird, Utah, April 2006• Invited paper, "Expanders and Nano-scaleSelf-assembly" (joint with A. Gamburd, M.Kang, P. Keukus, P. Vontobel), presentedby A. Gamburd.-United States-• Hot topics: Modularity for GL(n) andBeyond, MSRI, Berkeley, CA, October-Colloquium/Seminar/Workshop-Taiwan-• NCTS 2007 Winter School on NumberTheory, February 20071 lecture• NCTS Number Theory Seminar, September20061 lecture• NCTS 10th Anniversary Lecture Series inAlgebra and Number Theory, August 20072 lectures• Algebra Seminar, National TaiwanUniversity, October 20064 lectures• Colloquium, National Tsing-Hua University,October 20061 lecture• Colloquium, Tamkang University, March20071 lecture• Colloquium, National Chung-ChengUniversity, March 20072 lectures• Colloquium, National Chiao-TungUniversity, April 20071 lecture• Meet Female Mathematicians Workshop (forhigh school girls), Tung-Hai University, July20071 lecture-China-• Workshop on Coding Theory andActivities of onsite Scientists -›› 66

Cryptography, August 2007, Yangzhou,1 lecture• Morningside Center of Mathematics,Academia Sinica, Beijing, August 20071 lecture-Singapore-• Colloquium, National University ofSingapore, February 20071 lecture• Number theory Seminar, National Universityof Singapore, March 20071 lecture• Combinatorics Seminar, NanyangTechnological University, March 20071 lecture-Switzerland-• Special Year on "Limits of Graphs in GroupTheory and Computer Science", Bernoullicenter, EPFL, Lausanne, invited participants,April-May 20072 lecturesPublications• (joint with Ralf Koetter, Pascal O. Vontobel,and Judy Walker) Characterizations ofpseudo-codewords of LDPC codes,Advances in Math. 213, Issue 1 (2007), 205-229.• Recent Trends in Coding Theory withApplications, AMS/IP Proceedings series,editor, Providence (2007).• Upper and lower bounds for A(q). In: RecentTrends in Coding Theory and ItsApplications, AMS/IP Proceedings series,W. Li edited, Providence (2007), 15-23.• Elkies' modularity conjecture. In: RecentTrends in Coding Theory and ItsApplications, AMS/IP Proceedings series,W. Li edited, Providence (2007), 25-34.• Improved algebraic geometry bounds. In:Recent Trends in Coding Theory and ItsApplications, AMS/IP Proceedings series,W. Li edited, Providence (2007), 73-81.• (with Yotsanan Meemark) Hecke operatorson Drinfeld cusp forms, submitted.• (with Ming-Hsuan Kang) Zeta functions forfinite quotients of PGL(3), preprint, 2007III. Song-Sun LinNational Chiao Tung University,National Chair Professor and ChairProfessor of National Chiao-TungUniversity.Conferences and Visitings-Taiwan-• International Conference on Chaos andDynamical Complexity, May 24-30, 2006,CTS, Hsinchu, Taiwan.• 2007 CTS Workshop on Dynamical Systems,May 14-18, 2007, CTS, Hsinchu, Taiwan.-U.S.A.-• Harvard University, Professor S. T. Yau,August, 2006.-United Kingdom-• Heriot-Watt University, Edinburgh, July,2007.Publications• Smooth solutions to a class of quasilinearwave equations, J. Differential Equations,224(2006), 229-257. (with C.-H. Hsu and T.Makino)• Patterns generation and spatial entropy intwo-dimensional lattice models, to appear inAsian Journal of Mathematics (with J.-C.Ban and Y.-H. Lin).• Three-dmiensional cellular neural networksand patterns generation problems, to appearin International Journal of Bifurcation andChaos (with J.-C. Ban and Y.-H. Lin).IV. Wen-Wei LinNational Tsing-Hua UniversityTsing-Hua Chair professorTsing-Hua Professor of Natural Sciences67 ‹‹- Activities of onsite Scientists

Editor in Chief of Taiwanese Journal ofMathematics (2004--2006)Conferences and Visiting-China-• Dalian University of Technology, July-August, 2006 (Visiting).• Fudan University, August, 2006 (Visiting).• International Congress of ChineseMathematicians (ICCM2007), Hangzhou,China, December, 2007 (Invited Speaker).-Switzerland-• 6th International Congress on Industrial andApplied Mathematics (ICIAM2007), Zurich,Switzerland, July, 2007 (Invited Speaker).NCTS Activities• Recent Advances in Numerical Methods forEigenvalue Problems (RANMEP2008),NCTS Hsinchu, Taiwan, January, 2008(Organizer & Invited Speaker).Publications• Synchronization and Asynchronization inCoupled Lorenz-Type Maps, Int. J. Bifur.and Chaos, Vol. 16, No. 2 (2006), 269-280.(with S. F. Shieh and Y. Q. Wang)• Symmetric Preserving EigenvalueEmbedding in Finite Element ModelUpdating of Vibrating Structures, J. Soundand Vibration, Vol. 290(3-5) (2006), 839-864. (with J. Carvalho, B. N. Datta, and C. S.Wang)• Convergence Analysis of Structure-Preserving Doubling Algorithms for Riccati-Type Matrix Equations, SIAM Matrix Anal.Appl., Vol. 28, No. 1 (2006), 26-39. (with S.F. Xu)• New Methods for Finite Element ModelUpdating Problems, AIAA Jorunal, Vol. 44,No. 6 (2006), 1310-1316. (with Y. C. Kuoand S. F. Xu)• A Structure-Preserving Doubling Algorithmfor Nonsymmetric Algebraic RiccatiEquation, Numer. Math., Vol. 103, Issue 3(2006), 393-412. (with X.-X. Guo and S. F.Xu)• A Numerical Method for a GeneralizedAlgebraic Riccati Equation, SIAM ControlOptim, Vol. 45, No. 4 (2006), 1222-1250.(with D. L. Chu and R. C. E. Tan)• Solutions of the Partially Described InverseQuadratic Eigenvalue Problem, SIAMMatrix Anal. Appl., Vol. 29, No. 1 (2006),33-53. (with Y. C. Kuo and S. F. Xu)• Robust Partial Pole Assignment forVibrating Systems with AerodynamicEffects, IEEE Trans. Auto. Control, Vol. 51,Issue 12 (2006), 1979-1984. (with B. N.Datta and J. N. Wang)• Updating Quadratic Models with No Spill-Over Effect on Unmeasured Spectral Data,Inverse Problem, Vol. 23, Issue 1 (2007),243--256. (with M. T. Chu and S. F. Xu)• Projected Generalized Discrete-TimePeriodic Lyapunov Equations and BalancedRealization of Periodic Descriptor Systems,SIAM Matrix Anal. Appl., 2007, to appear.(with E. K. W. Chu and H. Y. Fan)• A Numerical Method for QuadraticEigenvalue Problems of GyroscopicSystems, J. Sound and Vibration, 2007, toappear. (with J. Qian)• Vibration of Fast Trains, PalindromicEigenvalue Problems and Structure-Preserving Doubling Algorithms, J. Comp.Appl. Math., 2007, to appear. (with E. K. W.Chu, T. M. Hwang, and C. T. Wu)V. Dong-Ho TsaiNational Tsing-Hua University, ProfessorInvited One-Month Research Professor atMSRI, Berkeley, USA, from August 14,2006 to May 18, 2007.Recent Invited TalkGeometric Evolution Equations andRelated Topics Seminar, MathematicalSciences Research Institute, September 6,Activities of onsite Scientists -›› 68

2006, Berkeley, USA.NCTS ActivityOrganizer of the "International Conferenceon Nonlinear Analysis", November 20-25,2006.Recent Publications• Tsai, D. H. (2005) Expanding embeddedplane curves, Contemporary Mathematics,American Mathematical Society, Vol. 367,189-227, 2005.• Tsai, D. H. (2005) Behavior of the gradientfor solutions of parabolic equations on thecircle, Calculus of Variations & PDE, Vol.23, 251-270, 2005.• Tsai, D. H. (2005) Asymptotic closeness tolimiting shapes for expanding embeddedplane curves, Inventiones Mathematicae,162, 473-492, 2005.• Nien, C. H., Tsai, D. H. (2006) ConvexCurves Moving Translationally in the Plane,Journal of Differential Equations, 225, 605-623, 2006.VI. Chin-Lung WangNational Central University, ProfessorNational Center for Theoretic Sciences,Shiing-shen Chern FellowConferences and Visiting-Taiwan-• Taipei (January-June): TIMS Seminars inRicci Flow.• Taipei (March): TIMS "Workshop on HigherDimensional Algebraic Geometry", coorganizerand invited speaker.• Taipei (June): "International Conference onGeometric Analysis", co-organizer(Forthcoming events)-Japan-• Tokyo (December): Algebraic GeometryConference at Tokyo University (organizer:Y. Kawamata), invited speaker.-China-• Hangzhou (December): ICCM2007 atZhejiang University, invited speaker.NCTS Activities• NCTS Summer School in AlgebraicGeometry, co-organizer (July 2007)• NCTS Student Seminar in AlgebraicGeometry, organizer (June-July, 2007)• NCTS 10 th Anniversary: Lecture Series onAlgebra and Number Theory (August, 2007)Research Works• Flops, motives and invariance of quantumrings, (with Y.-P. Lee and H.-W. Lin), toappear in Annals of Mathematics.• Elliptic functions, Green functions and themean field equations on tori, (with C.-S.Lin), submitted 2006.• Invariance of quantum ring under stratifiedMukai flops, (with B. Fu), in preparation.• Invariance of quantum rings under ordinaryflops, (with Y.-P. Lee and H.-W. Lin), inpreparation.VII. Jing YuNational Tsing-Hua UniversityNational Chair professorNational Central UniversityAdjunct Professor of MathematicsConferences-Taiwan-International Conference on Galoisrepresentations and function field Arithmetic(May 2007 at NCTS) Organizer.-China-International Conference on Langlands andgeometric Langlands program (June 2007Guanzhoa)• Invited Speaker, On Drinfeld modularityand automorphir representations.-Vietnam-69 ‹‹- Activities of onsite Scientists

International Conference on Number Theoryand related topics (December 2006, Hanoi)• Invited Speaker: Algebraic Independencein Positive characteristicNumber Theory Seminar/Workshop-Taiwan-• NCTS Number Theory Workshop (May2007), 1 lecture• 2007 Summer School on AutomorphirRepresentations (September 2007), 1 lecture• 2007 Winter School on Number Theory(February, 2007), 1 lecture-Korea-• Lectures on transcendence theory (February,2007, KAIST)Publications• Determination of algebraic relations amongspecial zeta values in positive characteristic(with Chieh-Yu Chang), Advances inMathematcis, 2007.• Algebraci independence of zeta values inpositive characteristic as the constant fieldvaries. (with Chieh-Yu Chang and M.Papanikolas), preprint 2007.• On class number relations in characteristictwo (with Yen-Mei J. Chen), Math. Zeit.2007.• On the independence of Heegner points inthe function field (with Fu-Tsun Wei),preprint 2007.E.2 Visiting ProfessorName: Der-Chen ChangGeorgetown University and NCTSActivities ParticipationDuring my visit at NCTS, I gave a series oflectures on "Subelliptic PDEs andsubRiemannian Geometry". I co-organized aWorkshop on Geometric Analysis withProfessor Shu-Cheng Chang from NationalTsing Hua University which was held at NCTSand CTS from January 16 to 18, 2007. Thespeakers were Professor Alexander Vasilievand Professor Irina Markina from Universityof Bergen, Norway; Professor Bernard Gaveaufrom Universite Paris 6; Professor PeterGreiner from University of Toronto; ProfessorChisato Iwasaki from University of Hyogo;Professor Kenro Furutani from ScienceUniversity of Tokyo; Professor Hung-LingChiu from Chung Yuan Christian University;Professor Jingzhi Tie from University ofGeorgia; Professor Shu-Cheng Chang fromTsing Hua University and myself. All speakersgave very nice talks on different topics in subellipticpartial differential equations and sub-Riemannian geometry, analysis on CRmanifolds, pseudo-differential operator and itsapplications to complex analysis.I was also invited to give talks at Workshopon Functional Analysis and HarmonicAnalysis which was held at National TaitungUniversity in January 2007 and InternationalConference in Geometric Analysis which washeld at Taida Institute of MathematicsSciences and NCTS Taipei Office in June18~22, 2007.Besides hat, I was invited to givecolloquium talks at many universities. Theseactivities give me opportunities to exchangeideas in mathematics with colleagues inTaiwan.Activities PromotionDuring March 5 to 6, 2007, I co-organizeda Workshop in Analysis and Geometry withProfessor Hsuan-Pei Lee and Professor Chin-Huey Chang at the Academia Sinica. Thespeakers were Professor Richard Beals fromYale University; Professor Bernard Gaveaufrom Universite Paris 6; Professor PeterGreiner from University of Toronto; ProfessorDe-Chi Wu from the Academia Sinica;Professor Chun-Chung Hsieh from theAcademia Sinica; Professor Jingzhi fromUniversity of Georgisa and me.I was invited to participate the evaluationprocess of the Mathematics Department atActivities of onsite Scientists -›› 70

Tsing Hua University and Fu Jen CatholicUniversity. These opportunities allowed me togive some input of my opinion onmathematical research and mathematicaleducation.Courses and Lectures on advanced topicsDuring my visit at NCTS, Professor Shu-Cheng Chang and I organized a mini-course atNCTS and CMS. Speakers and topics are:1. Professor Der-Chen Chang fromGeorgetown University, "Sub-elliptic PartialDifferential Equations and Sub-RiemannianGeometry".2. Professor Wen-Ling Huang from Universityof Hamburg, "The Positive MassConjecture".3. Professor Jiin-Chang Shaw from Chiao-Tung University "Quantum Mechanics".4. Professor Jih-Hsin Cheng from the CademiaSinica, "The Positive P-Mass Conjectureand CR Yamabe Problem".5. Professor Shu-Cheng Chang from TsingHua University, "The CR HarnarkEstimates"6. Professor Jianguo Cao from University ofNotre Dame, "Morse Theory of DistanceFunctions on Curved Spaces".We met every Friday from 10:30 am to12:00 pm and then 1:30 pm to 3:00 pm. Therewere many graduate students and faultymembers from differential university attendedthis mini-course.I had many chances to discuss mathematicsand their career development with graduatestudents at Tsing Hua University. One of themhas decided to work on his Ph.D. thesis undermy direction and in fact, has already arrivedMaryland. I gave a project to a Ph.D. studentat Tsing Hua University. He will come to visitme sometime in 2008 and try to finish thispaper.Current ProjectsI am working on subRiemannian geometryinduced by subelliptic partial differentialequations which arise especially from severalcomplex variables. During my visit at NCTS, Ihave chances to discuss a joint project withProfessor Shu-Cheng Chang at Tsing HuaUniversity and Professor Jin Shin Cheng at theAcademia Sinica. We are going to finish apaper on "Laguerre calculus and Paneitzoperator on the Heisenberg group".I am working on a joint project withProfessor Ming-Yee Lee from National CentralUniversity on "Estimates of generalizedCalder\'on-Zygmund operators in weightedspaces".During my visit at NCTS, I had finishedtwo papers with Professor Ovidiu Calin fromEastern Michigan University (who visitedNCTS last summer) on two papers: 1."Isometric embeddings of subRiemannianmanifolds in R m " which will appear inAdvanced Studies in ContemporaryMathematics. 2. "SubRiemannian geometry: avariation approach" which will appear inappear in Journal of Differential Geometry,(2007). Professor Calin has visited NCTS inthe summer of 2007 and will visit NCTS againduring 2008.I am finishing up two papers with anothertwo visitors: Professor Alexander Vasiliev andProfessor Irina Markina on "GeneralizedHamilton-Jacobi equation and heat kernel onstep two nilpotent Lie groups" and "Sub-Lorentzian Geometry on Anti-De Sitter Space".Invited TalksDuring my visit at NCTS, I have invited togive lectures at many universities andinstitutes in Taiwan, Hong Kong, China andJapan. Here is the list.1. Colloquium, Tunghai University, Taichung,Taiwan, January 3, 2007.2. Workshop on Geometric Analysis, NationalCenter for Theoretical Sciences, Hsinchu,Taiwan, January 16-18, 2007.3. Symposium on Analysis and Its AlgebraicStructures, National Taitung University,Taitung, Taiwan, January 22-23, 2007.4. Special Colloquium, Fu Jen CatholicUniversity, Taipei, Taiwan, January 31,71 ‹‹- Activities of onsite Scientists

2007.5. Colloquium, Taida Institute of MathematicalSciences, National Taiwan University,Taipei, Taiwan, February 5, 2007.6. Geometry Seminar, Institute ofMathematical Sciences, The University ofHong Kong, Hong Kong, February 8, 2007.7. Special Program in Analysis and Geometry,National Center for Theoretical Sciences,Hsinchu, Taiwan, March 2,9,16, 2007.8. Workshop in Analysis and Geometry,Academia Sinica, Taipei, Taiwan, March 5-6, 2007.9. Colloquium, Chung Yuan ChristianUniversity, Chung Li, Taiwan, March 9,2007.10. Colloquium, National Tsing HuaUniversity, Hsinchu, Taiwan, March 12,2007.11. Colloquium, Tunghai University,Taichung, Taiwan, March 14, 2007.12. Forum on Teaching Calculus, Fu JenCatholic University, Taipei, Taiwan, March19, 2007.13. Special Program in Analysis andGeometry, National Center for TheoreticalSciences, Hsinchu, Taiwan, April 13, 2007.14. Invited One Hour Address, Workshop inGeometric Analysis, University of Bergen,Bergen, Norway, May 4, 2007.15. Invited 45 minutes Address, InternationalConference on "New Trends on Complexand Harmonic Analysis", Voss, Norway,May 7-11, 2007.16. Invited One Hour Address, 2007International Conference on SeveralComplex Variables and ComplexGeometry, Xiamen University, Xiamen,China, May 28-31, 2007.17. Invited One Hour Address, Workshop onFunctional and Global Analysis, TokyoUniversity of Sciences, Tokyo, Japan, June4-6, 2007.18. Colloquium, Tamkang University, Taipei,Taiwan, June 12, 2007.19. Colloquium, National Central University,Chungli, Taiwan, June 14, 2007.20. Invited One Hour Address, InternationalConference on Geometric Analysis,National Taiwan University, Taipei,Taiwan, June 18, 2007.21. Colloquium, FuJen Catholic University,Taipei, Taiwan, June 25, 2007.22. Invited One Hour Address, Workshop inComplex Geometry, The University ofHong Kong, Hong Kong, China, July 10,2007.23. Eight lectures at summer school, WuhanUniversity, Wuhan, China, July 24-27,2007.24. Colloquium, Wuhan University ofTechnology, Wuhan, China, July 24, 2007.25. Colloquium, the Chinese Academy ofSciences, Wuhan Institute of Mathematics& Physics, Wuhan, China, July 25, 2007.26. Celebrating 10th anniversary of NCTSseries of lectures, National Center forTheoretical Sciences, Hsinchu, Taiwan,July 31, 2007.27. Special lecture on Game Theory, NationalChanghua Girl's High School, Changhua,Taiwan, August 6, 2007.CTS Preprints2007-8-002: DER-CHEN CHANG ANDSTEPHEN S.-T. YAU"EOMETRIC ANALYSIS ON AFAMILY OF PSEUDOCONVEXHYPERSURFACES"2007-7-002: DER-CHEN CHANG "BERGEN LECTURE ON ∂ – -NEUMANN PROBLEM "2007-7-001: OVIDIU CALIN, DER-CHENCHANG, IRINA MARKINA"GENERALIZEDHAMILTON-JACOBI EQUATION ANDHEAT KERNELON STEP TWONILPOTENT LIE GROUPS "2007-1-004: OVIDIU CALIN, DER-CHENActivities of onsite Scientists -›› 72

CHANG, IRINA MARKINA"GEOMETRIC ANALYSIS ONH-TYPE GROUPS RELATEDTO DIVISION ALGEBRAS "2007-1-003: Ovidiu Calin and Der-ChenChang "Isometric Embeddings ofSubRiemannian Manifolds in R m "2007-1-002: Ovidiu Calin, Der-Chen Changand Irina Markina"SubRiemannian geometry on thesphere S 3 "Lecture Notes2007 NCTS&CMS TopicalProgram in Analysis and Geometry:SubellipticPDEs and SubRiemannian Geometry(I)(II)(III)(IV)(V)(VI)(VII)E.3 Visiting Assistant ProfessorName: Guan-Yu ChenActivities Participation• NCTS Student Seminar on Probability(Organizer: 2006/7-2006/12)• NCTS 2007 Summer Course on Probabilisticand Statistic Methods in Bioinformatics(2007/7/5-2007/7/26)Academic VisitDepartment of Mathematics, CornellUniversity (3/1/2007-5/31/2007)Current Projects• The L 2 cutoff for reversible Markovprocesses and the comparison of discretetime and continuous time thresholds.• The logarithmic Sobolev constant for oddcycles and flat tori.• Algorithms for spectral gaps and logarithmicSobolev constants on finite birth and deathchains.Invited Talks• "The cutoff phenomenon for finite Markovchains",• "The logarithmic Sobolev constant on finitecycles", Analysis seminar in CornellUniversity, April 2007• "The L 2 cutoff for finite Markov chains",Probability seminar in Cornell University,April 2007NCTS Preprints• "The cutoff phenomenon for randomizedriffle shuffles", Joint with Laurent Saloff-Coste, NCTS preprint 2006. Accepted byRandom Structures and Algorithms.• "The cutoff phenomenon for ergodic Markovprocesses", Joint with Laurent Saloff-Coste,NCTS preprint 2007. Submitted.• "The logarithmic Sobolev constant of somefinite Markov chains", Joint with Wai-WaiLiu and Laurent Saloff-Coste, NCTSpreprint 2007. Accepted by Annales de laFaculte des Sciences de Toulouse.E.4 Report of Post DoctorsName: Yan-Hsiou ChengMy recent research focus on the nodalproblem and the spectral theory of the Sturm-Liouville problem. The second course, thespectral theory, is the topic I am studying inthe seminar held by Processor C.L. Shen inNational Tsing Hua Univresity. The researchof the nodal problem is a joint work withProfessor C.K. Law in National Sun Yat-senUniversity. We hope to apply the inverse nodaltheory to some other eigenvalue problems.During the past half year, I haveparticipated in the following academicactivities.Seminar/Visit/Conference1. I joint the seminar held by Processor C.L.Shen in NTHU. We discuss the spectralproblem of the general Sturm-Liouvilleproblems and also read some papers.2. I attended some of seminars held by NCTS.The topics include Harmonic Analysis,73 ‹‹- Activities of onsite Scientists

Math. Biology and Dynamical Systems,Bioinformatics and so forth.3. I will give a talk on October in TamkangUniversity.Future plans1. We hope to make the inverse nodal theoryperfect and take more applications on otherproblems. The existence problem in inversenodal problem is not solved yet and that iswhat we want to study actively.2. On the other hand, I hope that someinteresting problems will be discussed in theseminar with Processor C.L. Shen.Additionally, I wish to learn more techniqueand knowledge about my research.Name: Chian-Jen WangResearchMy research has been focusing onquestions related to the distinguishedrepresentations of metaplectic groups recently.Some of these questions have been studiedearlier in my thesis in the case where themetaplectic groups involved are four-foldcovers of GL(4). This year, I have extendedpart of the results obtained earlier in my thesisto metaplectic covers of GL(n), and fixedsome gaps there towards establishing thedesired distinguished representations on theGL(4) coverings.More specifically, this project involves alocal theory (Rankin-Selberg theory) and aglobal method (the converse theorem).Locally, we studied the Rankin-Selbergconvolutions for metaplectic groups andassigned local Gamma factors to metaplecticrepresentations. The analytic behaviors of thelocal Gamma factors were examined. Globally,we generalized the work of Cogdell-Piatetski-Shapiro on the converse theorems for GL(n) tometaplectic setting. Both of the local theoryand the global method have now been settledfor the n-fold covers of GL(n). As anapplication, we applied the converse theoremof metaplectic version combined with theanalytic information form the local theory toshow the existence of certain distinguishedrepresentations on the metaplectic covers ofGL(4), which generalize classical Thetafunctions. This project is expected to completeby the end of the year.For future research, I would like to studymetaplectic forms from different perspectives;for example, using the technique of traceformulas to gain better understanding of thenature of these metaplectic forms. I would alsolike to explore further the Fourier coefficientsof the distinguished representations, which areknown to carry rich arithmetic information.Talks/NCTS ActivitiesDuring this year, I gave four lectures on theconverse theorems for GL(n) in the workshopat NCTS, and three more lectures on theapplications of the converse theorems in thewinter school held at the Aspire Park,Taoyuan. I also gave talks regardingmetaplectic representations in the NumberTheory Seminar at NCTS and contributed atalk introducing metaplectic forms in theWorkshop on Algebra and Geometry atNCCU. These experiences have helped me toorganize and convey my ideas in a moreeffective way.At NCTS, I attended the Number TheorySeminar and Lie Theory Seminar regularly.There were several exciting activities held thisyear: the course on Modular Forms and GaloisRepresentations offered by Prof. Winnie Li inthe Fall semester, the international conferenceon Galois Representations and Function FieldArithmetic in May, the summer school andwinter school discussing topics ranging fromclass field theory, non-Archimedean geometry,Drinfeld modular forms to representationtheory, etc. Participating in these activities andtalking to number theorists local and fromabroad, I learned a lot and had fun.Papers and Preprints1. Chian-Jen Wang "Local Rankin-SelbergConvolutions for Metaplectic Groups"preprint.2. Chian-Jen Wang "Converse Theorems forMetaplectic Groups" preprint.Activities of onsite Scientists -›› 74

PreprintsSeries I2007-1-012007-1-022007-1-032007-1-042007-1-052007-1-062007-1-072007-1-082007-1-092007-1-102007-1-112007-1-122007-1-13Title and AuthorEfficient Numerical Schemes for Electronic States in CoupledQuantum DotsTsung-Min Hwang, Wei-Hua Wang, and Weichung WangMotivic Integration and Algebraic CyclesJyh-Haur TehStructured Doubling Algorithms for Weak Hermitian Solutions ofAlgebraic Riccati EquationsTsung-Min Hwang and Wen-Wei LinOn A Doubling Algorithm for The Nonlinear Matrix EquationX+A T X -1 A=Q when ⏐λ(X -1 A)⏐≤1Eric King-wah Chu, Tsung-Min Hwang, Wen-Wei Lin and Shu-Fang XuA Continuation Method for Positive Bound States of m-coupledNonlinear Schrödinger EquationsYuen-Cheng Kuo, Wen-Wei Lin, Shih-Feng Shieh and Weichung WangA Numerical Method for Quadratic Eigenvalue Problems ofGyroscopic SystemsJiang Qian and Wen-Wei LinSubRiemannian Geometry on the Sphere S 3Ovidiu Calin, Der-Chen Chang and Irina MarkinaIsometric Embeddings of SubRiemannian Manifolds in R mOvidiu Calin and Der-Chen ChangGeometric Analysis on H-type Groups Related to Division AlgebrasOvidiu Calin, Der-Chen Chang and Irina MarkinaVibration of Fast Trains, Palindromic Eigenvalue Problems andStructure-Preserving Doubling AlgorithmsEric King-wah Chu,Tsung-Min Hwang,Wen-Wei Lin and Chin-Tien WuA John-Nirenberg Type Inequality for Qα(Rn)Hong Yue and Galia DafniGeometric Quantization and Zuckerman Models of Semisimple LieGroupsMeng-Kiat ChuahCombinations of Collocation and Finite-Element Methods forPoisson's EquationHsin-Yun Hu and Zi-Cai Li75 ‹‹- Preprints

Series I2007-1-142007-1-152007-1-162007-1-172007-1-182007-1-192007-1-202007-1-212007-1-222007-1-232007-1-242007-1-252007-1-262007-1-272007-1-28Title and AuthorThe Spectrum of Chaotic Time Series(I): Fourier AnalysisGoong Chen, Sze-Bi Hsu, Yu Huang, and Marco A. Roque-Sol.The Spectrum of Chaotic Time Series(II): Fourier AnalysisGoong Chen, Sze-Bi Hsu, Yu Huang, and Marco A. Roque-Sol.The Final Size of a SARS Epidemic Model without QuarantineSze-Bi Hsu and Lih-ing W. RoegerNonlinear Dynamics Induced by Repetitive Optical Pulse Injection ofa Semiconductor LaserFan-Yi Lin, Shiou-Yuan Tu,Chien-Chih Huang, and Shu-Ming ChangA Structured Doubling Algorithm for Discrete-time AlgebraicRiccati Equations with Singular Control Weighting MatricesChun-Yueh Chiang, Hung-Yuan Fan and Wen-Wei LinGeneralized Hénon Maps and Half-orientable Smale HorseshoesSergey Gonchenko, Ming-Chia Li, Mikhail MalkinNumerically Stable, Structure-preserving Algorithms forPalindromic Quadratic Eigenvalue ProblemsJiang Qian, Tsung-Min Hwang and Wen-Wei LinOn a Simple Maximum Principle Technique Applied toEquations on the CircleYu-Chu Lin and Dong-Ho TsaiExpanding Immersed Convex Plane CurvesTai-Chia Lin, Chi-Cheung Poon, and Dong-Ho TsaiThe Cutoff Phenomenon for Ergodic Markov ProcessesGuan-Yu Chen and Laurent Saloff-CosteGeneralized Hamilton-Jacobi Equation and Heat Kernel on StepTwo Nilpotent Lie GroupsOvidiu Calin, Der-Chen Chang and Irina MarkinaBergen Lecture on ∂ – -Neumann ProblemDer-Chen ChangA Homology and Cohomology Theory for Real Projective VarietiesJyh-Haur TehThe Logarithmic Sobolev Constant of Some Finite Markov ChainsGuan-Yu Chen, Wai-Wai Liu and Laurent Saloff-CosteHeteroclinic Cycles in the Chemostat Models and the WinnerlessCompetition PrincipleSze-Bi Hsu and Lih-Ing W. RoegerPreprints -›› 76

Series I2007-1-292007-1-302007-1-312007-1-322007-1-332007-1-342007-1-352007-1-362007-1-372007-1-382007-1-392007-1-402007-1-41Title and AuthorStructure-preserving Arnoldi-type Algorithms for PalindromicQuadratic Eigenvalue ProblemsTsung-Min Hwang, Wen-Wei Lin and Jiang QianGeometric Analysis on a Family of Pseudoconvex HypersurfacesDer-Chen Chang and Stephen S.-T. YauAverage Values of L-functions in Characteristic TwoYen-Mei J. ChenOn the Independence of Heegner Points in the Function Field CaseFu-Tsun Wei and Jing YuCompetition of Two Host Species for a Single-limited ResourceMediated by ParasitesSze-Bi Hsu and I-Fan SunCompetitive Exclusion of Microbial Species for a Single-limitedResource with Internal StorageSze-Bi Hsu and Ting-Hao HsuOn the Role of Asymptomatic Infection in TransmissionDynamics of Infectious DiseasesSze-Bi Hsu and Ying-Hen HsiehGlobal Dynamics of a Predator-Prey Model with Hassell-VarleyType Functional ResponseSze-Bi Hsu, Tzy-Wei Hwang and Yang KuangConcentration Phenomena in a Nonlocal Quasilinear ProblemModelling Phytoplanktion in Poorly Mixed Water ColumnsYihong Du and Sze-Bi HsuThe Direct Integral of Some Weighted Bergman SpacesMeng-Kiat ChuahA Quick Proof on the Equivalence Classes of Extended VoganDiagramsMeng-Kiat Chuah and Chu-Chin HuPseudo-einstein and Q-flat Metrics with Eigenvalue Estimateson CR-hypersurfacesJianguo Cao and Shu-Cheng ChangThe Bondi-mass Type Estimate on a Closed CR 3-manifold withNonnegative Paneitz OperatorShu-Cheng Chang and Chin-Tung Wu77 ‹‹- Preprints

Series I2007-1-422007-1-432007-1-442007-1-452007-1-462007-1-472007-1-482007-1-492007-1-502007-1-512007-1-522007-1-532007-1-54Title and AuthorOn the CR Analogue of Obata's Theorem in a Pseudohermitian3-manifoldShu-Cheng Chang and Hung-Lin ChiuThe Li-Yau-Hamilton Inequality for Yamabe Flow on a Closed CR3-manifoldShu-Cheng Chang, Hung-Lin Chiu and Chin-Tung WuAlgebraic Independence of Carlitz Zeta Values for DifferentConstant FieldsChieh-Yu Chang, Matthew A. Papanikolas and Jing YuPeriod Polynomials and Explicit Formulas for Hecke Operatorson Γ 0 (2)Shinji Fukuhara and Yifan YangDetermination of Hauptmoduls and Construction of AbelianExtensions of Quadratic Number FieldsHung-Jen Chiang-Hsieh and Yifan YangDifferential Equations Satisfied by Modular Forms and K3SurfacesYifan Yang and Noriko YuiA Short Prooff of Milne's Formulae for Sums of Integer SquaresLing Long and Yifan YangOn Atkin and Swinnerton-dyer Congruence Relations (2)A.O.L. Atkin, Wen-Ching Winnie Li, and Ling LongHecke Operators on Drinfeld Cusp FormsWen-Ching Winnie Li and Yotsanan MeemarkSpreading Speeds and Traveling Waves for Non-monotoneIntegrodifference EquationsSze-Bi Hsu and Xiao-Qiang ZhaoFully Consistent and Accurate Pressure Boundary Conditionfor MAC Scheme on Curvilinear DomainsYin-Liang Huang, Jian-Guo Liu and Wei-Cheng WangExact Far Field Boundary Condition for Flows PastAxisymmetric ObstaclesYin-Liang Huang, Jian-Guo Liu and Wei-Cheng WangFast Solver for Scalar and Vector Poisson Equation onSpherical ShellsYin-Liang Huang, Jian-Guo Liu and Wei-Cheng WangPreprints -›› 78

Series II2007-2-01Title and AuthorMinimal Polynomials of Algebraic Derivations and AutomorphismsChen-Lian Chuang, Tsiu-Kwen Lee and Chi-Tsuen Yeh2007-2-02An Example of Bergman's and the Extension Problem for CleanRingsTsiu-Kwen Lee, Zhong Yi and Yiqiang Zhou2007-2-03Blowup Rate Estimates for the Heat Equation with a NonlinearGradient Source TermJong-Shenq Guo and Bei Hu2007-2-042007-2-052007-2-062007-2-072007-2-08Half-Skyrmions and Spike-Vortex Solutions of Two-componentNonlinear Schrodinger SystemsTai-Chia Lin and Juncheng WeiConstruction of Galois Covers of Curves with Groups of SL 2 -typeChia-Fu YuIrreducibility and p-adic Monodromies on the Siegel Moduli SpacesChia-Fu YuKottwitz-Rapoport Strata in the Siegel Moduli SpacesChia-Fu YuAn Exact Geometric Mass FormulaChia-Fu Yu2007-2-092007-2-10Hydrodynamic Limits of Two-component Gross-PitaevskiiEquations with Rotating Fields and Trap PotentialsTai-Chia Lin, Chiun-Chang LeeAlgebraic Prime Subalgebras in Simple Artinian AlgebrasTsiu-Kwen Lee and Yiqiang Zhou2007-2-11 Quotient Rings and f-radical Extensions of RingsChen-Lian Chuang, Tsiu-Kwen Lee and Cheng-Kai Liu2007-2-122007-2-13Operator Semi-Selfsimilar Processes Induced by Multi-dimensionalRandom Walk in Multi-dimensional Random SceneryTatsuhiko Saigo and Narn-Rueih ShiehQuotient Rings of Ore Extensions with More Than OneIndeterminateYuan-Tsung Tsai and Chen-Lian Chuang79 ‹‹- Preprints

Series III2007-3-012007-3-022007-3-032007-3-042007-3-052007-3-062007-3-072007-3-082007-3-092007-3-102007-3-112007-3-122007-3-132007-3-142007-3-152007-3-16Title and AuthorCircular Choosability Via Combinatorial NullstellensatzSerguei Norine, Tsai-Lien Wong, Xuding ZhuGame Colouring the Cartesian Product of GraphsXuding ZhuOn the Adaptable Chromatic Number of GraphsPavol Hell and Xuding ZhuBounds on Circular Consecutive ChoosabilitySerguei Norine, Zhishi Pan, Xuding ZhuAdapted List Coloring of Graphs and HypergraphsA.V. Kostochka and Xuding ZhuRefined Activation Strategy for the Marking GameXuding ZhuAn Algorithm for Semi-infinite Transportation ProblemsShen-Yu Chen and Soon-Yi WuAlgorithms for Infinite Quadratic Programming in L p SpacesShen-Yu Chen and Soon-Yi WuAn Explicit Exchange Algorithm for Linear Semi-infiniteProgramming Problems with Second-order Cone ConstraintsShunsuke Hayashi and Soon-Yi WuGap Functions for a System of Generalized Vector QuasiequilibriumProblems with Set-valued MappingsNan-Jing Huang, Jun Li and Soon-Yi WuA Finitely Terminating Explicit Exchange Method for ConvexSemi-infinite ProgrammingLiping Zhang, Soon-Yi Wu and Marco A. L´OpezRobust Envelope-constrained Filter with Orthonormal Basesand Semi-definite and Semi-infinite ProgrammingS. J. Li, K. L. Teo, X. Q. Yang and S. Y. WuFirst Order Optimality Conditions for Generalized Semi-infiniteProgramming ProblemsJ. Ye and S. Y. WuGateaux Differentiability of the Dual Gap Function of aVariational InequalityZ. L. Wu and S. Y. WuAn Infinite-dimensional Mathematical Programming Approachto Separation in Lp (X, A, M)M. Lopez, S. Y. Wu, C. Ling and L. QiAn Explicit Algorithm for Convex Semi-infinite ProgrammingProblem with Second-Order Cone ConstraintS. Hayashi and S. Y. WuPreprints -›› 80

Series III2007-3-172007-3-182007-3-192007-3-202007-3-212007-3-222007-3-232007-3-242007-3-252007-3-262007-3-272007-3-282007-3-292007-3-302007-3-312007-3-322007-3-33Title and AuthorIsing Vectors in the Vertex Operator Algebra VΛ + Associatedwith the Leech Lattice ΛChing Hung Lam and Hiroki ShimakuraQuantum Codes from Hadamard MatricesW.F. Ke, K.F. Lai, and R.B. ZhangA Characterization of The Moonshine Vertex Operator Algebraby Means of Virasoro FramesChing Hung Lam and Hiroshi YamauchiThe Structure of Compact Disjointness Preserving Operatorson Continuous FunctionsYing-Fen Lin and Ngai-Ching WongGeometric Pre-ordering on C*-AlgebrasChi-Wai Leung, Chi-Keung Ng and Ngai-Ching WongJordan Isomorphisms and Maps Preserving Spectra of CertainOperator ProductsJinchuan Hou, Chi-Kwong Li, and Ngai-Ching WongSeparating Linear Maps and Zero Product Preservers ofContinuous Fields of Banach Spaces and C*-AlgebrasChi-Wai Leung, Chi-Keung Ng, and Ngai-Ching WongThe Triangle of Operators, Topologies, BornologiesNgai-Ching WongGeometric Unitaries in Jb-AlgebrasChi-Wai Leung, Chi-Keung Ng and Ngai-Ching WongProperty T for Non-Unital C*-AlgebrasChi-Wai Leung, Chi-Keung Ng, Ngai-Ching WongA Banach-Stone Theorem for Riesz Isomorphisms of BanachLatticesJin Xi Chen, Zi Li Chen and Ngai-Ching WongOn C*-Algebras with Property TChi-Wai Leung, Chi-Keung Ng and Ngai-Ching WongUnitaries in Jb-AlgebrasChi-Wai Leung, Chi-Keung Ng and Ngai-Ching WongCompact Disjointness Preserving Maps of ContinuousFunctionsYin-Fen Lin and Ngai-Ching WongAmbarzumyan-type Theorems for the Sturm-LiouvilleOperator on Star-shaped GraphsC.K. Law and C.T. ShiehIntegrability of Rotationally Symmetric N-harmonic MapsChao-Nien Chen, L.F. Cheung, Y.S. Choi, C.K. LawReconstructing Potentials from Zeros of One EigenfunctionXinfu Chen, Y.H. Cheng, and C.K. Law81 ‹‹- Preprints

Series III2007-3-342007-3-352007-3-362007-3-372007-3-382007-3-392007-3-402007-3-412007-3-42Title and AuthorInverse Nodal Problems for Nonlinear Sturm-LiouvilleEquationsChao-Nien Chen and C.K. LawDistinguishing Labeling of Group ActionsTsai-Lien Wong and Xuding ZhuMulti-Colouring the Mycielskian of GraphsWensong Lin, Daphne Der-Fen Liu aAnd Xuding ZhuLower Bounds for the Game Colouring Number of Partial K-Trees and Planar GraphsJiaojiaowu and Xuding ZhuCartesian Powers of Graphs Can Be Distinguished by TwoLabelsSandi Klavzar and Xuding ZhuDistinguishing Labellings of Group Actionb on Vector Spacesand GraphsSandi Klavžar, Tsai-Lien Wong and Xuding ZhuMultiple Colouring of Cone GraphsZhishi Pan and Xuding ZhuThe D-Relaxed Game Chromatic Index of K-degeneratedGraphsHungyung Chang and Xuding ZhuDistinguishing Labeling of the Actions of Symmetric andAlternating GroupsTsai-Lien Wong and Xuding ZhuPreprints -›› 82

Visiting Mathematicians 20072007NameJiahong Wu(Oklahoma State University)M.H. Kang(Penn. State University)Field of InterestNonlinear Partial DifferentialEquationsNumber TheoryPeriod of Visit2006/09/01 ~ 2006/09/302006/09/03 ~ 2006/12/31AppendixKeiichi Komatsu(Waseda University)Number Theory2006/09/03 ~ 2006/09/16Yasushi Mizusawa(Sophia University)Number Theory2006/09/03 ~ 2006/09/16Wu-Yi Hsiang(Hong Kong University ofScience and Technology)Differential geometry2006/09/04 ~ 2006/09/11Yu Huang(Zhongshan SUN YAT SENUniversity)Dynamical System2006/09/12 ~ 2006/10/11Alain Perronnet(Universite de Paris VI & VII)Finite elements scientificcomputation2006/09/12 ~ 2006/10/01Edmund R. Puczylowski( University of Warsaw, Poland)Algebra(Ring Theory)2006/09/12 ~ 2006/10/01Ser Peow Tan(National University ofSingapore)Geometry2006/09/22 ~ 2006/10/01Charles Li(Academia Sinica)Algebra2006/09/25 ~ 2006/09/30Yakov Alber(Technion-Israel Institute ofTechnology)Functional Analysis2006/10/05 ~ 2006/11/06Frank Hwang(ATT and National Chiao TungUniversity)Dicsrete Mathematics2006/10/10 ~ 2006/10/18Joseph Silverman(Brown University)Number Theory2006/10/15 ~ 2006/10/28Xiaojiao Tong(Changsha University of Science& Technology)Optimization2006/10/15 ~ 2006/11/15Xie-Ping Ding(Sichuan Normal University)Functional Analysis2006/10/24 ~ 2006/11/2383 ‹‹- Appendix

AppendixGurjar Rajendra Vasant(Tata Institute of FundamentalResearch)Chia-Fu Yu(Academia Sinica)2007Name Field of Interest Period of VisitAlgebraic Geometry 2006/10/25 ~ 2006/11/14Geometry 2006/10/25 ~ 2006/10/27Yongzeng (George) Lai(Wilfrid Laurier University)Financial Mathematics 2006/11/06 ~ 2006/11/26Toshihiro Uemura(University of Hyogo)Probability 2006/11/08 ~ 2006/11/16Peter Sasieni(Cancer Research UK) Biostatistics 2006/11/14 ~ 2006/11/16Dongho Chae(Sungkyunkwan University)PDE 2006/11/15 ~ 2006/11/20Kazuhiro Ishige(Tohoku University) PDE 2006/11/16 ~ 2006/11/20Dong-Ho Chae(Seoul National University) Nonlinear PDE 2006/11/20 ~ 2006/11/25Michel Chipot(Institute für MathematikUniversitüt Zürich)P. G. Ciarlet(City University of Hong Kong)Applied Mathematics,Dynamical System,Nonlinear PDE,Scientific Computation,Applied Mathematics,Differential Geometry2006/11/20 ~ 2006/11/252006/11/20 ~ 2006/11/21N. Kenmochi(Chiba University) Nonlinear PDE 2006/11/20 ~ 2006/11/25David Kinderlehrer(Carnegie Mellon University) Nonlinear PDE 2006/11/20 ~ 2006/11/25Y. Morita(Ryukoku University)W.-M. Ni(University of Minnesota)Mythily Rawasmany(T. I. F. R. Center)Applied Mathematics 2006/11/20 ~ 2006/11/25Nonlinear PDE 2006/11/20 ~ 2006/11/25Nonlinear PDE 2006/11/20 ~ 2006/11/25Kunimochi Sakamoto(Hiroshima University)Itai Shafrir(Technion-Israel Institute ofTechnology)Dynamical System,Nonlinear PDENonlinear PDE2006/11/20 ~ 2006/11/252006/11/20 ~ 2006/11/25Appendix -›› 84

S. Ukai(City University of Hong Kong)Juncheng Wei(Chinese University of HongKong)Algebraic Geometry 2006/10/25 ~ 2006/11/14Eiji Yanagida(Tohoku University) Nonlinear PDE 2006/11/20 ~ 2006/11/25Bogdan Bojarski(Polish Academy of Sciences) Nonlinear PDE 2006/11/21 ~ 2006/11/22Z. Xin(Chinese University of HongKong)Nonlinear PDE 2006/11/21 ~ 2006/11/25Bogdan Bojarski(Polish Academy of Sciences) PDE 2006/11/22 ~ 2006/12/11Mitsuharu OTANI(Waseda University)Yoshikazu Giga(University of Tokyo)Shih-Hsien Yu(City University of Hong Kong)Yoshitsugu Kabeya(Osaka Prefecture University)Alex Novikov(University of Technology,Sydney)Eric Chu(Monash University, AU)S. Schaible(University of California,Riverside)2007Name Field of Interest Period of VisitApplied Mathematics,Nonlinear PDEApplied Mathematics,Dynamical System2006/11/22 ~ 2006/11/25Nonlinear PDE 2006/11/23 ~ 2006/11/25Nonlinear PDE 2006/11/23 ~ 2006/11/25PDE 2006/11/25 ~ 2006/12/03Probability 2006/11/26 ~ 2006/12/08Scientific computation 2006/12/01 ~ 2007/01/09Chuu-Lian Terng(University of California, Irvine) Geometry 2006/12/02 ~ 2006/12/10Optimization and Controltheory2006/11/20 ~ 2006/11/252006/12/08 ~ 2007/01/02Shengjie Li(Chongqing University)Optimization 2006/12/10 ~ 2007/01/09Nikolai N. Leonenko(Cardiff University) Probability 2006/12/13 ~ 2006/12/27Meng-Kiat Chua(National Chiao TungUniversity)Algebra 2006/12/14 ~ 2006/12/25AppendixReyer Sjamaar(Cornell University)Optimization 2006/12/14 ~ 2006/12/2785 ‹‹- Appendix

AppendixYuan Lou(Ohio State University)Dinakar Ramakrishnan(California Institute ofTechnology)Chiu-Yen Kao(The Ohio State University)2007Name Field of Interest Period of VisitPDE 2006/12/16 ~ 2006/12/20Algebraic Geometry,Number Theory,Automorphic Forms2006/12/17 ~ 2006/12/19Scientific Computing 2006/12/18 ~ 2006/12/29Jun Zou(National University ofSingapore)Bei Hu(University of Notre Dame)Yen-His Tsai(The University of Texas atAustin)Shuyu Sun(Clemson University)Zhidong Bai(National University ofSingapore)King Fai Lai(Sydney University)Galia Dafni(Concordia University)Discrete Mathematics 2006/12/18 ~ 2006/12/24PDE 2006/12/19 ~ 2007/01/03Scientific Computing 2006/12/19 ~ 2007/01/14Finite element methods 2006/12/20 ~ 2007/01/08Discrete Mathematics 2006/12/21 ~ 2006/12/30Algebra 2006/12/22 ~ 2006/12/25Analysis 2006/12/25 ~ 2007/01/07Henri Darmon(Mc Gill University) Number Theory 2006/12/25 ~ 2007/01/01Wentang Kuo(University of Waterloo Canada)Irina Markina(University of Bergen)Alexander Vasiliev(University of Bergen)Number Theory,Representation TheoryDifferential Geometry &Geometric Analysis,Real AnalysisDifferential Geometry &Geometric Analysis,Math. Physics2006/12/25 ~ 2007/01/072007/01/04 ~ 2007/01/282007/01/04 ~ 2007/01/28Alexandr Vasilievich Kostochka(University of Illinois at Urbana-Champaign)Discrete Mathematics 2007/01/05 ~ 2007/01/15Appendix -›› 86

2007Name Field of Interest Period of VisitJie Sun(Nat'l Univ. of Singapore) Optimization 2007/01/05 ~ 2007/01/11Eric K.-W. Chu(Monash University, AU)Kenro Furutani(Science University of Tokyo)Optimization 2007/01/10 ~ 2007/01/23Differential Geometry &Geometric Analysis2007/01/10 ~ 2007/01/24AppendixChisato Iwasaki(University of Hyogo )Differential Geometry &Geometric Analysis2007/01/10 ~ 2007/01/24Marco Lopez(Alicante University, Spain)Hidekazu Niibori(Tsukuba University)H. Shimakura(Hokkaido University)Hiroshi Yamauchi(University of Tokyo)Zhi Lu(FuDan University)Optimization 2007/01/10 ~ 2007/01/21Algebra 2007/01/14 ~ 2007/01/19Algebra 2007/01/14 ~ 2007/01/19Algebra 2007/01/14 ~ 2007/01/19Geometry 2007/01/15 ~ 2007/01/28Jie Xiao(Tsinghua University)Quantum Group,Ringel-Hall Algebras2007/01/15 ~ 2007/01/23Jae-Hoon Kwon( University of Seoul) Algebra 2007/01/18 ~ 2007/01/18Magnus Aspenberg(University Paris-Sud)Geometry 2007/01/21 ~ 2007/02/04Nikolaos Kavallaris(Osaka University) PDE 2007/01/22 ~ 2007/01/29Dimitrios Tzanetis(National Technical Universityof Athens)Wen-ling Huang(University of Hamburg)PDE 2007/01/22 ~ 2007/01/29Geometry and Math. Physics 2007/02/24 ~ 2007/03/17Richard W. Beals(Yale University)Analysis,Partial Differential Equations2007/02/27 ~ 2007/03/1887 ‹‹- Appendix

AppendixKoichiro Harada(Ohio State University)Shunsuke Hayashi(Kyoto University)Bernard Brighi(University of Haute Alsace)2007Name Field of Interest Period of VisitAlgebra 2007/03/01 ~ 2007/03/25Optimization 2007/03/01 ~ 2007/03/15PDE 2007/03/10 ~ 2007/03/20Sergey Norin(Georgia Institute ofTechnology)Discrete Mathematics 2007/03/11 ~ 2007/03/23Yihong Du(University of New England)Dynamical System,Mathematical Biology,Nonlinear PDE2007/03/15 ~ 2007/04/26Peter Horak(University of Washington,Tacoma)Chuu-Lian Terng(University of California, Irvine)Chen Ling(Zhejiang University of Finance& Economics)Hiroshi Matano(University of Tokyo)Discrete Mathematics 2007/03/16 ~ 2007/03/29Geometry 2007/03/16 ~ 2007/03/22Optimization 2007/03/17 ~ 2007/05/17PDE 2007/03/18 ~ 2007/03/23Boris Kouniavski(Bar-Ilan University)Galois cohomology,algebra,algebraic geometry, numbertheory2007/03/22 ~ 2007/04/05Meng Chen(Fudan University)Algebraic geometry 2007/03/23 ~ 2007/04/15Tommaso De Fernex(University of Utah) Algebraic geometry 2007/03/26 ~ 2007/04/01James Mckernan(University of California atSanta Barbara)Higher dimensional geometry 2007/03/26 ~ 2007/04/01Jason Michael Starr(Stony Brook University)Birational geomerty 2007/03/26 ~ 2007/04/01Bao-Hua Fu Algebraic geometry 2007/03/27 ~ 2007/04/02Wu-Yi Hsiang(University of California,Berkeley)Transformation group,Differential geometry2007/03/27 ~ 2007/04/02Appendix -›› 88

Der-Chen Chang(Georgetown University) Classical Analysis 2007/04/12 ~ 2007/04/15Der-Chen Chang(Georgetown University)2007Name Field of Interest Period of VisitClassical Analysis 2007/04/18 ~ 2007/04/19Francois Jean Raymond Hamel(University of Aix-Marseille III) PDE 2007/04/21 ~ 2007/04/29AppendixKing Fai Lai(University of Sydney)Xiaoqiang Zhao(memorial University ofNewfoundland)Boyan Slavchev Sirakov(The University of Paris 10)Shigeharu Takayama(University of Tokyo)Song Ping Zhu(University of Wollongong)Number Theory 2007/04/23 ~ 2007/05/23Dynamical System,Mathematical Biology,Nonlinear Differential,EquationsElliptic and parabolic PDE andapplications 2007/04/29 ~ 2007/05/08Mathematical andComputational Finance2007/04/27 ~ 2007/05/28Geometry 2007/04/30 ~ 2007/05/072007/05/02 ~ 2007/05/04So-Hsiang Chou(Bowling Green state University)Numerical Analysis of PDEs,Fluid Dynamics relatedapplications, Mathematics ofFinance2007/05/03 ~ 2007/08/03Vjacheslav Yurko(Saratov University) Differential Equations 2007/05/03 ~ 2007/05/06H. L. Smith(Arizona State University)Dynamical System,Mathematical Biology2007/05/06 ~ 2007/05/20Dinesh S. Thakur(University of Arizona U.S.A.)Algebraic Geometry,Number Theory2007/05/06 ~ 2007/05/18Pawel Pilarczyk(Rutgers University) Dynamical System 2007/05/09 ~ 2007/05/19Piotr Zgliczynski(Jagiellonian University) Dynamical System 2007/05/09 ~ 2007/05/22Eusebius Doedel(Concordia University) Dynamical System 2007/05/11 ~ 2007/05/27Arnaldo Garcia(IMPA, Brasil) Number Theory & Coding 2007/05/11 ~ 2007/05/25David Savitt(University of Arizona) Number Theory 2007/05/11 ~ 2007/05/2489 ‹‹- Appendix

AppendixW. Dale Brownawell(Penn. State University)Matthew A. Papanikolas(Texas A&M University)Frits Beukres(Utrecht University)2007Name Field of Interest Period of VisitNumber Theory 2007/05/12 ~ 2007/05/25Number Theory 2007/05/12 ~ 2007/05/22Number Theory 2007/05/13 ~ 2007/05/27Gebhard Boeckle(University Essen)Jinqiao Duan(Illinois Institute of Technology)Number Theory 2007/05/13 ~ 2007/05/19Dynamical System 2007/05/13 ~ 2007/05/18M.H. Kang(Penn. State University) Number Theory 2007/05/13 ~ 2007/08/13Ling Long(Iowa State University)Richard Moeckel(University of Minnesota)Number Theory 2007/05/13 ~ 2007/05/31Dynamical System 2007/05/13 ~ 2007/05/18Gareth E. Roberts(College of the Holy Cross) Dynamical System 2007/05/13 ~ 2007/05/18Chia-Fu Yu(Academia Sinica, and Max-Planck Institute, Bonn)Number Theory 2007/05/13 ~ 2007/05/18Jiu-Kang Yu(Purdue University)Number Theory &Representation Theory2007/05/13 ~ 2007/05/19Anthony To-Ming Lau(University of Alberta,Edmonton, Alberta, Canada)David Gao(Virgina Institute of Technology)Functional Analysis 2007/05/17 ~ 2007/06/04Optimization 2007/05/20 ~ 2007/06/04Heng Huat Chan(National University ofSingapore)Jiu-Kang Yu(Purdue University)Analytic Number Theory, BasicHypergeometric Series, EllipticFunctionsNumber Theory &Representation Theory2007/05/21 ~ 2007/05/302007/05/21 ~ 2007/06/02Siu-Hung NG(lowa State University)Algebra 2007/05/22 ~ 2007/05/29Chieh-Yu Chang(National Tsing-Hua University) Number Theory 2007/06/01 ~ 2007/07/31Appendix -›› 90

2007Name Field of Interest Period of VisitLih-Ing Wu Roeger(Texas Tech University) Mathematical Biology 2007/06/01 ~ 2007/07/04Yi-Giang Zhou(Memorial University ofNewfoundland)Ring theory, Module theory 2007/06/01 ~ 2007/06/30Marc Eric Raimondo(University of Sydney)Statistics 2007/06/02 ~ 2007/06/15Yongsheng Han(Auburn University)Harmonic Analysis 2007/06/03 ~ 2007/06/23Genaro Lopez Acedo(University of Seville, Spain) Functional Analysis 2007/06/05 ~ 2007/06/12AppendixJian-Guo Liu(University of Maryland)Kee Hoon Kang(University of Georgia) Statistics 2007/06/06 ~ 2007/06/15P. Greiner(University of Toronto)Analysis 2007/06/08 ~ 2007/06/29Laurent Cavalier(University Aix-Marseille 1) Statistics 2007/06/09 ~ 2007/06/17Liu Yu(University of Science andTechnology Beijing)Applied Mathematics,Nonlinear PDE,Scientific Computation2007/06/05 ~ 2007/06/30Harmonic Analysis 007/06/10 ~ 2007/08/31Ren-Jun Duan(City University of Singapore)Luen-Fai Tam(\The Chinese University ofHong Kong)Boltzmann equation 2007/06/15 ~ 2007/07/15Differential Equations 2007/06/15 ~ 2007/06/18Khee Meng Koh(National University ofSingapore)Duong H. Phong(Columbia University, USA) Geometric analysis 2007/06/16 ~ 2007/06/23Grahame Bennett(Indiana University)Harmonic Analysis 2007/06/17 ~ 2007/07/07Eric Chu(Monash University, AU)Scientific Computation 2007/06/17~ 2007/07/15Eric Grinberg(Temple University)Tsung-Ming Hwang(National Taiwan NormalUniversity)Graph theory, Lattice theory 2007/06/16 ~ 2007/06/29Geometric Analysis,Integral Geometry2007/06/17 ~ 2007/06/23Scientific Computation 2007/06/17 ~ 2007/09/1691 ‹‹- Appendix

AppendixLei Ni(University of California, SanDiego)Stephen Shing-Toung Yau(University of Illinois)Huai-Dong Cao(Lehigh University)Chen-Yu Chi(Harvard University)Peter Wai Kwong Li(University of California)Jia-Ping Wang(University of Minnesota)Sanming Zhou(University of Melbourne)Shun-Jen Cheng(Academia Sinica)Stephen S. T. Yau(University of Illinois atChicago)2007Name Field of Interest Period of VisitGeometric analysis 2007/06/17 ~ 2007/06/23Algebraic geometry 2007/06/17 ~ 2007/06/23Geometric analysis 2007/06/18 ~ 2007/06/23Algebraic Geometry 2007/06/18 ~ 2007/08/18Geometry analysis 2007/06/18 ~ 2007/06/22Geometry analysis 2007/06/18 ~ 2007/06/22Discrete Mathematics 2007/06/19 ~ 2007/06/22Optimization 2007/06/22 ~ 2007/06/23Geometry 2007/06/23 ~ 2007/06/26Der-Fen Liu(California State University)Silvia Petra Heubach(California State University)Kwang-Ming Hwang(National Chiao TungUniversity)San-Ming Zhou(University of Melbourne)Sheng Bau(Fuzhou University)Wai-Hong Chan(Hong Kong Baptist University)Bei-Fang Chen(Hong Kong University ofScience and Technology)Rong-Quan Feng(Peking University)Wen-Jie He(Hebei University ofTechnology)Graph Theory andCombinatoricsGraph Theory andCombinatoricsCombinatorial Optimization,Discrete Mathematics,Communication NetworksGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatorics2007/06/20 ~ 2007/06/302007/06/21 ~ 2007/07/012007/06/21 ~ 2007/06/302007/06/22 ~ 2007/06/302007/06/23 ~ 2007/06/292007/06/23 ~ 2007/06/282007/06/23 ~ 2007/06/282007/06/23 ~ 2007/07/042007/06/23 ~ 2007/07/01Appendix -›› 92

Weng-Song Lin(Southeast University)Mei Lu(Tsinghua University)Chee Wai Shiu(Hong Kong Baptist University)Zhi-Wei Sun(Nanjing University)Jian-Fang Wang(Chinese Academy of Science)Kai-Shun Wang(Beijing Normal University)Tao Wang(Nankai University)Da-Qing Yang(Fuzhou University)Xing-Xing Yu(Georgia Institute ofTechnology)He-Ping Zhang(Lanzhou University)Xiao-Dong Zhang(Shanghai JiaoTong University)Zhong-Fu Zhang(Lanzhou Jiaotong University)Yi Zhao(Georgia State University)Chang-Hong Lu(East China Normal University)Katsuya Miyake(Waseda University)Duong H. Phong(Columbia University)Yong-Qiang Zhao(Shijiazhuang College)Geng-Hua Fan(Fuzhou University)2007Name Field of Interest Period of VisitGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatoricsGraph Theory andCombinatorics2007/06/23 ~ 2007/06/302007/06/23 ~ 2007/06/302007/06/23 ~ 2007/06/282007/06/23 ~ 2007/06/302007/06/23 ~ 2007/06/292007/06/23 ~ 2007/07/042007/06/23 ~ 2007/06/302007/06/23 ~ 2007/06/30007/06/23 ~ 2007/06/272007/06/23 ~ 2007/06/302007/06/24 ~ 2007/06/29Number Theory 2007/06/24 ~ 2007/07/03Complex analysis andgeometry, MathematicalPhysicsGraph Theory andCombinatoricsGraph Theory andCombinatorics2007/06/23 ~ 2007/06/302007/06/23 ~ 2007/06/302007/06/23 ~ 2007/06/30Akinari Hoshi(Waseda University) Number Theory 2007/06/24 ~ 2007/06/282007/06/24 ~ 2007/06/272007/06/24 ~ 2007/06/292007/06/25 ~ 2007/06/30Appendix93 ‹‹- Appendix

2007Name Field of Interest Period of VisitAppendixCai Leizhen(Chinese University of HongKong)Hua Mao(Hebei University)Thomas Simon Mountford(Ecole Polttechnique Fédérale deLausanne)Changyuan Cheng(National Pingtung University ofEducation)Paolo Cascini(University of California atSanta Barbara)Bao Qin Li(Florida InternationalUniversity)Chin-Tung Wu(National Pingtung University ofEducation)Graph Theory andCombinatoricsGraph Theory andCombinatorics2007/06/25 ~ 2007/06/30Prorobability and statistics 2007/06/25 ~ 2007/07/05Dynamical System 2007/07/01 ~ 2007/08/30Algebraic Geometry 2007/07/02 ~ 2007/07/09Complex Analysis 2007/07/09 ~ 2007/07/29Differential Geometry andGeometric Analysis2007/06/25 ~ 2007/07/02Yuan-Pin Lee(University of Utah) Algebraic Geometry 2007/06/26 ~ 2007/07/31Wensong Lin(Southeast University) Discrete Mathematics 2007/06/30 ~ 2007/07/23Daqing Yang(Fuzhou University)Discrete Mathematics 2007/06/30 ~ 2007/07/23Wei-Chen Yao(TMUE)Number Theory 2007/07/01 ~ 2007/07/31Masayuki Kawakita(RIMS)Algebraic Geometry 2007/07/02 ~ 2007/07/13Motoko Kawakita(Kyoto University)Algebraic Geometry 2007/07/02 ~ 2007/07/08Caucher Birkar(Cambridge University)Algebraic Geometry 2007/07/04 ~ 2007/07/13Yum-Tong Siu(Harvard University) Complex Geometry 2007/07/04 ~ 2007/07/04Wayne M. Eby(Temple University) Harmonic Analysis 2007/07/06 ~ 2007/07/122007/07/10 ~ 2007/09/09Hoshi Akinari(Waseda University)Generic polynomial, Genericdimension, Noether's problem,Rationality problem, Invarianttheory, Tschirnhausentransformation, Cremona group2007/07/17 ~ 2007/07/27Appendix -›› 94

Ngaiming Mok(University of Hong Kong)Algebraic Geometry,Differential Geometry2007/07/20 ~ 2007/07/21Wen-Hsiung Li(University of Chicago) Bioinformatics 2007/07/27 ~ 2007/07/28Yen-His Tsai(The University of Texas atAustin)Jann-Long Chern(National Central University)Shing-Tung Yau(Harvard University)2007Name Field of Interest Period of VisitScientific Computing 2007/07/31 ~ 2007/08/25Nonlinear PDE 2007/08/01 ~ 2008/07/31Algebraic Geometry,Applied Mathematics,Differential Geometry andGeometric Analysis,Number Theory, Algebra,Representation Theory andRelated Topics,Scientific Computation2007/08/01 ~ 2007/08/06AppendixXue-Xiang Huang(School of Management, FudanUniversity)Kainam Thomas Wong(Hong Kong PolytechnicUniversity)Shunsuke Hayashi(Kyoto University)Functional Analysis 2007/08/06 ~ 2007/09/02Discrete Mathematics 2007/08/06 ~ 2007/08/09Optimization 2007/08/09 ~ 2007/08/24Wenxun Xing(Tsinghua University, Beijing) Optimization 2007/08/10 ~ 2007/08/20Chiu-Yen Kao(The Ohio State University)Douglas W. Vestal(University of Califormia, SantaBarbara)Ching-Li Chai(University of Pennsylvania)Dan'l Pierce(Access Analytics Int'l)Edmund R. Puczylowski(University of Warsaw)Krzysztof Stempak(Politechnika Wroclawska)Scientific Computing 2007/08/13 ~ 2007/09/10Financial Mathematics 2007/08/15 ~ 2007/09/15Number Theory 2007/08/18 ~ 2007/08/29Scientific Computation 2007/08/20 ~ 2007/08/24Algebra(Ring Theory) 007/08/22 ~ 2007/09/21Harmonic Analysis 2007/08/24 ~ 2007/09/1095 ‹‹- Appendix

AppendixJing-Song Huang(HKUST) Representation Groups 2007/08/29 ~ 2007/08/31Eiji Yanagida(Tohoku University)2007Name Field of Interest Period of VisitDifferential Equations 2007/08/30 ~ 2007/09/08Xun-Hua Gong(Nanchang University) Functional Analysis 2007/09/01 ~ 2007/09/30Wei Zhu(Rice University, Zurich)Geometric Measure Theory,Calculus of Variations, PartialDifferential Equations2007/09/01 ~ 2007/09/30Richard Schoen(Stanford University)Differential Geometry, Partialdifferential equations2007/09/13 ~ 2007/09/26Emilio Acerbi(University of Parma) Calculus of variations, PDE 2007/09/20 ~ 2007/10/03S.M Bhatwaddekar(Indian National ScienceAcademy)Yoshihito Oshita(Okayama University)Mikhail Chebotar(Kent state University)Commutative algebra 2007/10/01 ~ 2007/10/28PDE 2007/10/15 ~ 2007/10/21Ring Theory,LinearAlgebra,Operator Algebra 2007/12/10 ~ 2008/01/09Appendix -›› 96

NCTS 2007 Conference, Workshop & SchoolTime Conference & Workshop PlaceSept. 4-14, 2006NCTS Short Course on Introduction toIwasawa TheorySpeaker: Keiichi Komatsu (WasedaUniversity, Japan)Lecture Room of NCTS,National Tsing HuaUniv.AppendixSept. 13, 2006-Jan. 12, 2007Topical Program in Modular Forms andGalois RepresentationsSpeaker: W. –C. Li (NCTS and Penn. StateU.)Lecture Room of NCTS,National Tsing HuaUniv.Sept. 14-Dec. 30, 2006Topical Program in Symmetries in Chaosand Molecular Quantum MechanicsSpeaker: Goong Chen (Texas A&MUniversity)Lecture Room of NCTS,National Tsing HuaUniv.Nov. 8, 2006NCTS Forum Mathematics Research inTaiwanChandler Davis (U. Toronto & Math.Intelligencer) Hung-Lin Fu (NCTU)Sze-Bi Hsu (NTHU) Wen-Ching WinnieLi (NCTS&NTHU) Chang-Shou Lin(TIMS&NTU) Song-Sun Lin(NCTS&NCTU) Wen-Wei Lin(NCTS&NTHU) Pei Yuan Wu (NCTU)Jing Yu (NCTS&NTHU)Lecture Room of NCTS,National Tsing HuaUniv.Nov. 9, 2006Math. in 21th CenturyS. T. Yau (Harvard University)Lecture Room of NCTS,National Tsing HuaUniv.Nov. 15-22, 2006NCTS Workshop on the ConverseTheorems for GLnOrganizer: Jing Yu (NCTU & NTHU)Lecture Room of NCTS,National Tsing HuaUniv.Nov. 20-25, 2006International Conference on NonlinearAnalysisORGANIZING COMMITTEE:C.-C. Chen (Taipei ) M. Chipot(Zurich) P.G. Ciarlet (HongKong) J.-S. Guo (Taipei )N. Kenmochi (Chiba) C.-S. Lin(Chai-Yi ) X. Pan (Shanghai )D.-H. Tsai (Hsinchu) Z. Xin(Hong Kong) E. Yanagida(Sendai )Lecture Room of NCTS,National Tsing HuaUniv.97 ‹‹- Appendix

AppendixDec. 1-2, 2006Time Conference & Workshop PlaceNational Taiwan NormalUniv.January 16-18, 20072007 NCTS & CMS WorkshopGeometric AnalysisOrganizer: Der-Chen Chang (GeorgetownUniv. & NCTS)Shu-Cheng Chang (NTHU)Lecture Room of NCTS,National Tsing HuaUniv.January 18, 2007Mini Workshop on Lie algebra andrepresentation theoryOrganizer: Ching-Hung Lam (NCKU)National Cheng KungUniv.Feb. 2-6, 20072007 Winter School on Number TheoryOrganizer: Jing Yu (NCTU & NTHU)Aspire Park, TaoyuanMarch~Dec.,20072007 A Series of Seminars onOptimization with EngineeringApplicationsJein-Shan ChenNational Taiwan NormalUniv.March 2- June 29,2007Workshop on Reaction-Diffusion:Theory and Applicationsin honor of Masayasu Mimura's 65thBirthdayInvited Speakers:Chiun-Chuan Chen (NationalTaiwan University) Shin-IchiroEi (Kyushu University) Jong-Shenq Guo (National TaiwanNormal University) Yuzo Hosono(Kyoto Sangyo University) Tai-Chia Lin (National TaiwanUniversity) Masayasu Mimura(Meiji University) Toshi Ogawa(Osaka University) Dong-Ho Tsai(National Tsing Hua University)Je-Chiang Tsai (National ChungCheng University)NCTS Topical Program in Analysis andGeometrySpeaker: Der-Chen Chang (GeorgetownUniv.) Jiin-Chang Shaw(NCTU) Wen-Ling Huang(University of Hamburg) Jih-Hsin Cheng (Academia Sinica)Shu-Cheng Chang (NTHU)Jianguo Cao (Univ. of NotreDame)Lecture Room of NCTS,National Tsing HuaUniv.Appendix -›› 98

March 22- April 19,2007March 27-31, 2007May 9-10, 2007Time Conference & Workshop PlaceNCTS An Intensive Course in Reaction -Diffusion Systems with Application toSpatial EcologySpeaker: Yihong Du (University of NewEngland, Australia)Workshop on Higher DimensioanlAlgebraic GeometryOrganizers: Jungkai Alfred Chen (TaiwanU. & TIMS) Juin-ChengChen (NTHU& NCTS) Chin-Lung Wang (Central Univ. &NCTS)NCTS Mini--Workshop on MathematicalBiologyOrganizers:Sze-Bi Hsu (Tsing-HuaUniversity)Hal Smith (Arizona StateUniversity)Lecture Room of NCTS,National Tsing HuaUniv.National Taiwan Univ.Lecture Room of NCTS,National Tsing HuaUniv.AppendixMay 14-17, 2007May 14-18 , 2007May 24, 2007June 6-20, 2007June 13-Aug. 29, 20072007 NCTS Conference on GaloisRepresentations and Function FieldArithmeticOrganizers: Wen-Ching Winnie Li (PennState U & NCTS)Jing Yu (NCTS & NTHU)2007 NCTS Workshop on DynamicalSystemsOrganizers: Kuo-Chang Chen (NTHU)Jong Juang (NCTU)Ming-Chia Li (NCTU)Chih-Wen Shih (NCTU)NCTS & NCU Colloquium on NumberTheorySpeaker: Prof. W. Dale Brownawell (PennState University)Prof. Frits Beukers (University ofUtrecht)NCTS Series Lectures in HarmonicAnalysis: Multi-parameter FourierAnalysis I-VProf. Y. Han (Auburn University)NCTS Topical Program in HarmonicAnalysisSpeaker: Yu Liu (University of Science andTechnology Beijing)Lecture Room of NCTS,National Tsing HuaUniv.Lecture Room of NCTS,National Tsing HuaUniv.Lecture Room of NCTS,National Tsing HuaUniv.Lecture Room of NCTS,National Tsing HuaUniv.Lecture Room of NCTS,National Tsing HuaUniv& Math. epartment,National Central Univ.99 ‹‹- Appendix

Time Conference & Workshop PlaceAppendixJune 18-22, 2007International Conference on GeometricAnalysisOrganizers: Nai-Chung Conan Leung(Chinese U.) Jiaping Wang(U. of Minnesota) Mu-TaoWang (Columbia U.) Mao-Pei Tsui (U. of Toledo) Shu-Cheng Chang (NTHU) Jih-Hsin Cheng(AS) Yng-IngLee (NTU) Chin-Lung Wang(NCU)National Taiwan Univ.June 20, 2007Workshop on Graph Theory andNetworkOrganizer: Xuding Zhu (NSYSU)National Sun Yat-SenUniv.June 21-July 24, 2007A Short Course on Finite ElementMethods and Eigenvalue ProblemsSpeaker: So-Hsiang Chou (Bowling GreenState University)Lecture Room of NCTS,National Tsing HuaUniv.June 22-July 6, 2007NCTS Series Lectures in HarmonicAnalysisSpeaker: Grahame Bennett (IndianaUniversity)Lecture Room of NCTS,National Tsing HuaUniv.June 24-29, 20072007 International & Fourth Cross-straitConference on Graph Theory andCombinatoricsOrganizer: Gerard J. Chang (NTU)William Y. C. Chen (NankaiU.) Genghua Fan (FuzhouU.) Hung-Lin Fu (NCTU)Tayuan Huang (NCTU) Ko-Wei Lih (AS) Xuding Zhu(National Sun Yat-sen U.)National Taiwan Univ.June 27, 28, July 2,2007NCTS Short Course on Number TheorySpeaker: Katsuya Miyake (WasedaUniversity)Lecture Room of NCTS,National Tsing HuaUniv.July 3-12, 20072007 NCTS Mini-Course in AlgebraicGeometrySpeaker: Caucher Birkar (Univ. ofCambridge) Paolo Cascini (UCSanta Barbara) Jung-Kai Chen(NTU) M. Kawakita (RIMS)Lecture Room of NCTS,National Tsing HuaUniv.Appendix -›› 100

Time Conference & Workshop PlaceJuly 3, 10, 11, 13, 2007July 4, 2007NCTS Algebraic ComputationWorkshopSpeaker: Jing Yu (NCTS)Wei-Chen Yao (Taipei MunicipalUniversity of Education)NCTS 10th Year Anniversary SpecialLectures:Multiplier Ideal Sheaves andTheir Applications to Analysis andAlgebraic GeometrySpeaker: Yum-Tong Siu (HarvardUniversity)Lecture Room of NCTS,National Tsing HuaUniv.Lecture Room of NCTS,National Tsing HuaUniv.AppendixJuly 5-26, 2007NCTS Summer Course on Probabilisticand Statistic Methods in BioinformaticsOrganizers: Yuan-Chung Sheu (NCTU)Lecture Room of NCTS,National Tsing HuaUniv.July 17-18, 2007NCTS Mini Course on Lie AlgebraFrom Linear Algebra to Lie AlgebraSpeaker: Meng-Kiat Chuah (NTHU)Lecture Room of NCTS,National Tsing HuaUniv.July 20, 2007NCTS 10th Anniversary SpecialLectures: From boundary values ofbounded holomorphic functions to thegeometric theory of minimal rationalcurvesSpeakers: Ngaiming Mok (The Universityof Hong Kong)Lecture Room of NCTS,National Tsing HuaUniv.July 23, 2007NCTS 10 Years Anniversary Mini-Workshop on PDEHung-Chi Kuo (Department ofAtmospheric Sciences, NTU)Chun-Hsiung Hsia (University of Illinois atChicago)Horng-Tzer Yau (Harvard University)National Taiwan Univ.July 27, 2007NCTS 10th Anniversary SpecialLectures: Computational identificationof regulatory elements in yeastSpeaker: Wen-Hsiung Li (University ofChicago)Lecture Room of NCTS,National Tsing HuaUniv.July 31, 2007NCTS 10th Anniversary SpecialLectures: Hardy Spaces and EllipticBoundary Value ProblemSpeaker: Der-Chen Chang (NCTS &Georgetown Univ.)Lecture Room of NCTS,National Tsing HuaUniv.101 ‹‹- Appendix

AppendixTime Conference & Workshop PlaceAug. 1, 15, 22, 30,2007NCTS 10 Year Anniversary: LectureSeries on Algebra and Number TheorySpeaker: Chin-Li Chai (University ofPenn) Jing-Song Huang(HKUST) Winnie Wen-Ching Li(NCTS & Penn State U.) Chin-Lung Wang (NCTS & NationalCentral U.)Lecture Room of NCTS,National Tsing HuaUniv.Aug 2, 2007Aug. 3, 2007Aug. 7-28, 2007Sept. 3, 2007NCTS 10th Anniversary Special PlenaryLectures: Constructions of GeometricStructures on ManifoldsSpeaker: Shing-Tung Yau (HarvardUniversity)NCTS 10th Anniversary Special PublicLecture: Geometry, Nonlinear Analysisand Theoretical PhysicsSpeaker: Shing-Tung Yau (HarvardUniversity)NCTS 2007 Summer Course onDynamical SystemsSpeaker: Kuo-Chang Chen (NTHU)Chang-Yuan Cheng (NPUE)Shyan-Shiou Chen (NTNU)Wen-Chiao Cheng (NCCU)NCTS 10th Anniversary--Growth SeriesLecturesSpeaker: Kuo-Chang Chen (NTHU)Cheng-Hsiung Hsu (NCU)Ching-Hung Lam (NCKU)Hui-Wen Lin (NCU)Lecture Room of NCTS,National Tsing HuaUniv.Lecture Room of NCTS,National Tsing HuaUniv.Lecture Room of NCTS,National Tsing HuaUniv.Lecture Room of NCTS,National Tsing HuaUniv.Appendix -›› 102

Physics Division

Report of the Division HeadGeneral Remarksn the past year the operation of theNCTS Physics Division basicallyfollows the mode set up by the ex-director,Professor Tu-Nan Chang, aiming at her shorttermobjects: to nurture the next generationof theoretical scientists in Taiwan and toencourage interaction and collaborationamong participants. The user-initiatedacademic programs by the focus groups havebeen run smoothly, and made easier for groupmembers to access NCTS resources withhigher flexibility. The scientific activities andoutcomes of each focus group will besummarized in this report (see also at theNCTS web-site http://phys.cts.nthu.edu.tw/).The highlights of the NCTS PhysicsDivision in the past year include the evaluationand the restructure of the focus groups, theestablishment of the Young Theorist Award,the recruitment of outstanding scientific staff,and the promotion of internationalcollaborations with prestigious physicscenters. More details will be given later. It isan encouraging expansion of our centerscientist program that two brilliant youngphysicists, Professors Yueh-Nan Chen andChung-Hsien Chou, have been recruited bySubproject II at National Cheng-KungUniversity (NCKU)I want to take this opportunity to welcomeProfessors Chung-Yu Mou from NationalTsing-Hua University (NTHU) and Chon-Saar Chu from National Chiao-TungUniversity (NCTU), who have kindly acceptedthe duty of serving as the head and the deputyhead of the Physics Division, respectively,starting on Aug. 1 st , 2007. Another keydevelopment is that the Physics Division willmove into the more spacious fifth floor of thethird General Building at NTHU after thesummer of 2007 (the Mathematics Division islocated at the fourth floor). More coherentcooperation between the Mathematics andPhysics Divisions is expected in the future.Approximately two-ninth and one-ninth ofthe NCTS annual budget are channeledthrough Subproject I at National TaiwanUniversity (NTU), and Subproject II atNCKU, respectively, to support the activitiesof a few selected focus groups (four atSubproject I and three at Subproject II in2007.) The rest of the NCTS budget isallocated to the main project to support theactivities of other focus groups, the NCTSscientific personnel, and the additional NCTSsponsored functions, such as the jointprograms between Physics and MathematicsDivision.Executive Committee and YoungTheorist AwardThe Executive Committee composed ofChing-Ray Chang of NTU, Hai-Yang Chengof Academia Sinica (AS), Der-San Chuu ofNCTU, Hsiang-nan Li (chairman), Sy-SangLiaw of National Chung-Hsing University(NCHU), and Wei-Ming Zhang of NCKU,who represent the host institutes of the mainproject and the subprojects of NCTS, theinstitute that sponsors NCTS programs, andthe institute from the middle of Taiwan.Moreover, they also represent various fields intheoretical physics, providing opinions andsuggestions based on their expertise, andserving as the second reviewers of applicationsand recruitments submitted to NCTS.In order to encourage young colleagues topursue theoretical research, to maintain activeand to produce excellent works, we establishedthe Young Theorist Award in the Fall of 2006.The Mathematics Division also joins thiseffort, wishing that this award will soonbecome as prestigious as the Ta-You WuReport of the Division Head -›› 104

Fellowship of National Science Council (NSC)and the Young Scholar Award of AcademiaSinica (AS). The Executive Committee hasselected Professors Chi-Tin Shih of Tung-HaiUniversity and Daw-Wei Wang of NationalTsing Hua University as the recipients in 2007Focus Groups and Scientific ActivitiesThe majority of the NCTS scientificactivities are planned and carried out by theNCTS affiliated focus groups. More resourcesare allocated to sponsor workshops andschools targeting at students and juniorscientists with emphasis on new ideas andconcepts of emerging research subjects. Ourinternational visitors are encouraged andarranged to spend more time for informaldiscussion with the focus group membersduring their visit. Interactions among focusgroups have also increased with more jointactivities. All NCTS sponsored activities havebeen posted on the NCTS web-site athttp://phys.cts.nthu.edu.tw/ as soon as it isplanned, and also stayed on the web-siteafterwards as a future reference. Through theinternet network, we should be able tocommunicate openly and continuously withthe larger theoretical science community.The policies for supporting long-termvisitors (including multi-year internationalsenior visitors) and for recruiting postdoctoralfellows have been slightly modified. Not onlythe candidates for the above two categoriesneed to be recommended and nominated, buttheir stations are determined by the focusgroups themselves. With this additionalflexibility, we hope that the interaction amongvisitors, postdoctoral fellows, and the focusgroups can be further enhanced. Following thesame design, the responsibility of executingthe domestic visitor program, whichencourages active participation by facultymembers and research staff from universities,colleges, and other institutes with limitedresearch resources and opportunities, has beenalso assigned to the focus groups.After two years in operation under thecurrent NCTS structure, we have conducted asystematic performance evaluation of all focusgroups at the end of 2006. A PerformanceEvaluation Panel (PEP) was called for toperform the detailed academic evaluation withthe inputs from external reviewers based onthe criteria recommended and endorsed byboth the Executive Committee and theProgram Committee. One of the key criteriaemphasizes the progress made by the focusgroups through the expenditure of the NCTSresource. The evaluation was then submitted tothe Executive Committee at mid-December,2006 as the basis of restructuring the focusgroups and of adjusting their budget for thenext fiscal year.The restructure of the focus groups issummarized as follows. "System Biology"and"Nonlinear Phenomena in Physical andBiological Systems" were separated. Theformer was then combined with "Soft-BioMatters Physics", forming the new group"Softmatter, Biophysics and System Biology"."Strongly Correlated Electron Systems" and"Spin-related Physics in Condensed Matter"were combined into "Novel QuantumPhenomena in Condensed Matter". "PlasmaPhysics" is now classified as a working group,whose purpose and evaluation standards differfrom those for a focus group. The mission of aworking group is to attract and coordinatemanpower, and to educate young generation ina smaller research field, while a focus groupaims at production of works with significantimpact. The coordinators of some focus groupshave been changed too.Scientific Staff and InternationalCollaborationWe have expanded our center scientistprogram this year. Hsiu-Hau Lin (NTHU),Kingman Cheung (NTHU), Anatoly. G.Mal'shukov (NCTU), Chi-Jen David Lin(NCTU) have been appointed by the ExecutiveCommittee and by their home departments asthe center scientists. The appointment ofCheng-Hung Chang (NCTU), which was firstmade in early 2005, has been renewed. Asenior center scientist is demanded by the105 ‹‹- Report of the Division Head

leadership in his research field, while a juniorcenter scientist is entitled to be protected fromthe administrative and teaching loads. Twobrilliant young theoretical physicists,Professors Yueh-Nan Chen and Chung-HsienChou, were recruited by Subproject II atNCKU. Their appointment marks a substantialcontribution to our center scientist program.To attract experienced foreign researchersto work in Taiwan for a longer period, a newposition under the title "Staff Scientist" hasbeen created at NCTS this year. It is a nontenuretrack faculty position with researchfund, travel grant, and a postdoctoral quotafrom NCTS. Professor Kazuyuki Furuuchi,being highly recommended by externalreviewers and by the Executive Committee,has been recruited as our first staff scientist.Searching for the second candidate is now inprocess.The international collaborations withforeign prestigious physics centers have beenpromoted greatly this year. We shall organizeour first KITP-type topic program on"Superconductivity and Magnetism atNanoscale" in December of 2007 as a jointactivity with the Argonne National Laboratory.The coordinator from our side is ProfessorBaruch Rosenstein of NCTU. The number ofoutstanding visitors stationing at NCTU willremain several every week. A host is assignedto each visitor to guarantee his interaction withlocal community. The success of this programwill set up an example for other fields tofollow in the future. APCTP has invited us tosubmit a joint proposal for a Focus Program on"Astroparticle and Nuclear Physics" in 2008.NCTS will co-sponsor the KITP Program on"Advanced Topics on Flavor Physics" in thesummer of 2008 held at the Kavli Institute forTheoretical Physics, China.In addition to the center and staff scientists,assistant research scholars at NCTS includeDr. Je-An Gu ( , Cosmology), Dr.Shih-Yuin Lin ( , Gravitation), Dr.Kazutomu Shiokawa (Quantum InformationSciences), Dr. Yi Yang ( , Strings), Dr.Tzu Chiang Yuan ( , Particle Physics).Postdoctoral fellows include Dr. TakayukiHirayama (Strings), Dr. Hung-Cheuk Ho (, Atomic Physics), Dr. Wen-Hsuen Kuan( , Atomic Physics), Dr. Kao-Chin Lin( , Condensed Matter Physics), Dr. Yu-Pin Luo ( , Biophysics).Administrative StaffThere is no change both in personnel andjob assignment involving our supporting staffat NCTS. Sherry Sieu-Huey Pang ( )is responsible for the administrative affairs inPhysics at NCTS. Jia-yi Hsu ( ) isresponsible for the financial management.Hetty Chang ( ) and Meirue Shi () are assigned to provide logistics supportand to coordinate the scientific activities forthe focus groups. Chia-chi Liu ( ) andAnnie Lin ( ) are responsible for thelogistics and administrative support atsubprojects I and II, respectively. Theresponse to the service provided by our stafffrom our target community is uniformlypositive under the current "one-window"structure. We are grateful to their dedication.Concluding RemarksSimilar to what was stated last year, theNCTS is again blessed with a firmcommitment from NSC and the NCTS Boardof Directors and a tremendous support from arobust physics community in Taiwan this year.We have enjoyed a strong partnership with ourhost institutes NTHU, NCTU, NTU, NCKU,and AS. It is a good sign that NCTS hasprovided an important assistance in bothresearch and administration to our theoreticalphysics community. We have seen asubstantial increase in scientific activities andthe development of more focused researchdirections, which target at our immediateobjectives. I am confident that with a newleadership under Professors Chung-Yu Mouand Chon-Saar Chu, the NCTS PhysicsDivision will enjoy another successful year in2008 and many years beyond.Hsiang-nan Li ( )October 2007Report of the Division Head -›› 106

Speacial Report on the Symposium on the 10thAnniversary of NCTSWritten by: Chung-Yu Mouhe NCTS has entered the 10 th yearsince its establishment in 1997.During the past 10 years, NCTS has helped inshaping the research of theoretical physics inTaiwan. It is therefore an excellent occasion tocelebrate and overview the contribution ofNCTS. A symposium on the 10th Anniversaryof NCTS, organized by the Physics Division,was held on September 3 and 4, followed bythe inauguration of Physics New Offices onthe 5 th floor in the 3rd General Building. Allresearchers who worked at the physics divisionand former directors and divisional heads wereinvited and a reunion dinner was held.Distinguished guests and directors fromYukawa Institute for Theoretical Physics, AsiaPacific Center for Theoretical Physics, KoreanInstitute for Advanced Study, Kavli Institutefor Theoretical Physics China were alsoinvited to participate the symposium.In the morning of Sept. 3, minister Chien-Jen Chen of NSC came and gave openingaddress. Following his address, President Chenof NTHU, Vice President Lee of NCTU anddistinguished guests/directors from centers inAsia gave addresses for this particularoccasion. There was also nice retrospect ofNCTS by former divisional heads, Prof. Ting-Kuo Lee and Prof. Tu-Nan Chang.Currentdivisional head, Prof. Chung-Yu Mou, alsogave an overview what has been achieved byNCTS during the past nine years. The OCPAAAA / Robert T. Poe Prize was presented tothe former divisional head, Prof. Hsiang-NanLi, for his contribution on perturbed QCD. Theinauguration of Physics New Offices on the 5 thfloor in the 3 rd General Building was heldfollowing these speeches. Technical sessions(see detailed program in below) withpresentation of scientific results associatedwith the physics division were held later in theafternoon and on Sept. 4.Inaguration of new office (from left to right): Director JingYu (NCTS), President Wen-Tsuen Chen (NTHU), VicePresident Chia-Hoang Lee (NCTU), Deputy Minister Hung-Duen Yang(NSC)A scene of new office located at the 5th floor of 3rdGeneral Building, National Tsing Hua University107 ‹‹- Report of the Division Head

Distinguished guests from Asia famous institutes onthe celebration of NCTS 10th anniversary (from left toright): Director Yue-Liang Wu (KITPC), Director TohruEguchi (YITP), Director Ki-Myeong Lee (Phys. School,KIAS)Presentation of the OCPA AAA / Robert T. Poe Prize(from left to right): Professor Tu-Nan Chang (formerDirector of NCTS, USC), Prof. Hsiang-Nan Li (formerPhys. div. head of NCTS)

Highlights of ProgramsComplex SystemFocus Group on Critical Phenomena andComplex SystemsCoordinator: Chin-Kun Hu (Academia Sinica; email: huck@phys.sinica.edu.tw)Committee members: Shu-Chiuan Chang (National Cheng Kung University), Chi-Ming Chen (National Taiwan Normal University),Chi-Ning Chen (National Dong Hwa University), Shu-Heng Chen (National Chengchi University),Chung-I Chou (Chinese Culture University), Ming-Chung Ho (National Kaoshiung Normal University),Ming-Chang Huang (Chung-Yuan Christian University), I-Ming Jiang (National Sun-Yat Sen University),hai-Yu Lin (National Chung Cheng University), Ning-Ning Pan (National Taiwan University),Wen-Jer Tzeng (Tamkang University), Ming-Chya Wu (National Central University)I. Brief Descriptionhe purpose of this focused group is towork on various model systems togain a better understanding of criticalphenomena and then apply the methods andconcepts from such studies to interdisciplinaryproblems, especially the complex systems. Theproblems to be studied include: (1) latticemodels of critical systems (such as Ising,Potts, dimer models, spin glass, etc), (2) chaos,synchronization, and non-equilibrium process,(3) networks and self-organized criticalsystems (such as sandpile model), (4) structureand properties of biological macromolecules(such as DNA, RNA, and protein), (5)molecular biological evolution models, and (6)models for economic and social systems.Since members of this FG scatter indifferent universities and research institutes,the main academic activities of this FG includesix 2 3 days workshops and one InternationalWorkshop on Biological Physics and ComplexSystems on 6-11 August 2007. In eachworkshop, some invitors from other countrieswere invited to give a series of talks on topicsrelated to the interest of this FG. Somemembers of our FG and researchers in Taiwanwere also invited to give talks so that relatedresearch problems can be discussed. Someforeign visitors also work with researchers ofthis FG on join research problems.In 2007, the key active members of this FGinclude Professor Shu-Chiuan Chang (NationalCheng-Kung University), Professor Wen-CheTzeng (Tamkang University), Dr. Ming-ChyaWu (National Central University), Hsin-ChangChi (Department of Applied Science, NationalHualien University of Education), Dr. Jung-Hsin Lin (Research Center for AppliedSciences, Academia Sinica), Prof. Jui-Ling Yu(Dept. of Applied Math., ProvidenceUniversity)II. Activities1. From March to August 2007, we haveorganized four 2007 NCTS Workshop onCritical Phenomena and Complex Systems.Highlights of Programs -›› 110

The program of the workshops can be foundat http://www.sinica.edu.tw/?statphys/activities/workshop.html.2. We had organized 2007 TaiwanInternational Workshop on BiologicalPhysics and Complex Systems 6-11 August2007, at Institute of Physics, AcademiaSinica, Taipei. The program of theworkshop can be found athttp://www.phys.sinica.edu.tw/~statphys/activities/ conference/2007/3. We are organizing 2007 NCTS WorkshopOctober Workshop on 12, 13, and 15October. At this workshop, Professor KenseiKobayashi (Graduate School ofEngineering, Yokohama NationalUniversity, JAPAN) will give two 80minutes talks on "Chemical Evolution fromComplex Organics in Space to Life", whichis a very interesting and stimulating topic.Some other speakers from USA, France,Poland and Taiwan have been invited togive talks on protein research and complexsystems.4. In December 2007, we will organize anotherworkshop.5. We have organized a series of seminars andgroup meetings on critical phenomena andcomplex systems at Physics Departmentof Chung-Yuan Cristian University andInstitute of Physics of Academia Sinica.III. Visitors and InternationalCollaborations1. Prof. Shu-Chiuan Chang (PhysicsDepartment, National Cheng KungUniversity) visited NCTS (North) duringwinter and summer breaks. He alreadypublished two papers in J. Stat. Phys., andInt. J. Mod. Phys. B on Spanning trees onthe Sierpinski gasket (with Prof. Lung-ChiChen in Department of Mathematics, Fu JenCatholic University) and zeros of the Pottsmodel partition function in the large-q limit(with Professor Robert Shrock at SUNYStony Brook).1. Prof. Chang and Lung-Chi Chen alsoworked on enumerating the number ofdimers on the Sierpinski gasket withpossible vacancies on the outmost vertices.They derived rigorously such numbers andthe corresponding entropies on the twodimensionalSierpinski gasket and itsgeneralization with three, four and fivelayers. The upper and lower bounds of theentropies for the three, four and fivedimensional Sierpinski gaskets are alsoobtained. This work will be submitted forpublication soon.2. Prof. Tzeng Wen-Jer (Tamkang Univ, DeptPhys) visited NCTS (North) during summerand winter break. He worked on geneticswitch in periodic-changing environments.3. Prof. Hsin-Chang Chi (Deaprtment ofApplied Science, National HualienUniversity of Education) visited NCTS(North) during summer break. He and Prof.K. N. Huang of Academia Sinica usedrelativistic many-body perturbation theoryto calculate energy levels and transitionprobabilities of molecules. A research paperis under preparation.4. Olga S. Rozanova (Mathematics andMechanics faculty, Moscow StateUniversity, RUSSIA) visited NCTS (North)during summer break. She and Prof. Jui-Ling Yu (Dept. of Applied Math.,Providence University, a visitor at Instituteof Physics of Academia Sinica during summerbreak) worked on a model typhoontrajectories and a manuscript is underpreparation.5. Dr. Philippe Arnaud1 (Laboratoire deChimie de Coordination du CNRS, France)visited NCTS (North) in October 2006. Heand Dr. Jung-Hsin Lin (Research Center forApplied Sciences, Academia Sinica) areusing docking and molecular dynamicssimulations to study the targeting oftelomeres by small molecules, which isnowadays one the most promising strategiesfor the discovery of new antitumoral drugs.They continue the cooperation and willfinish a paper in the near future.6. Dr. N. Sh. Izmailian (Yerevan Institute of111 ‹‹- Highlights of Programs

Physics) visited NCTS (North) in early2007. He and Dr. Chin-Kun Hu finished apaper for co-evolution of virus and immunesystem, which was published in [Phys. Rev.E 75, 041104 (2007)]. They also worked ona paper about finite-size effects for the Isingmodel on the helical tori, which will appearin [Phys. Rev. E 76 (2007)].7. Zbigniew Struzik (Graduate School ofEducation, The University of Tokyo) visitedNCTS (North) in March 2007. He, Dr.Ming-Chya Wu (National CentralUniversity), and Dr. Chin- Kun Hu finisheda paper on temporal evolution for the phasehistogram of ECG during human ventricularfibrillation, which was published in AIPConference Proceedings 922 (AIP, NewYork, 2007) edited by M. Tacano, Y.Yamamoto, and M. Nakao, pp. 573-576. Anew version of the paper which takes intoaccount the survival probability is underpreparation and will be sent to a journal forpublication in the near future.IV. Highlights of Research Results1. RNA folding is a very difficulty theoreticalproblem. Most earlier studies neglectpseudo knots in the theoretical calculations.E. Sh. Mamasakhlisov (a visitor of this FG),Shura Hayryan, and Chin-Kun Hu includedpseudo knots in the calculation and studiedRNA folding in the presence of counterions.They found that the freezing and meltingtemperature of RNA decrease linearly withthe logarithm of the ion strength [Phys. Rev.E75, 061907 (2007)], which is consistentwith experimental observation.2. Under partial support by NCTS (North),Prof. David B. Saakian (Yerevan PhysicsInstitute) had visited NCTS (North) andInstitute of Physics of Academia Sinicaseveral times since 2004. He and Dr. Chin-Kun Hu published several papers at Proc.Natl. Acad. Sci. USA, Phys. Rev. E, and J.Stat. Phys.. In these papers, very generalfitness functions for biological evolutionmodels have been studied. Hu was invited togive a talk at 19th International Conferenceon Noise and Fluctuations on 9-14September 2007 in Tokyo on "Quantum andlattice models of biological evolution". Thebrief text of the talk was published at AIPConference Proceedings 922 (AIP, NewYork, 2007) edited by M. Tacano, Y.Yamamoto, and M. Nakao, pp. 589-594.3. Prof. Chi-Tin Shih (Physics Department,Tanghai University), Stephan Roche (CEA,France), and Rudolf A. Romer (Universityof Warwick, UK) studied point mutationseffects on charge transfer properties in theDNA sequence of the tumor-suppressor p53gene. On the basis of effective single-strandor double-strand tight-binding models whichsimulate hole propagation along the DNA, astatistical analysis of charge transmissionmodulations associated with all possiblepoint mutations is performed. They that incontrast to non-cancerous mutations,mutation hotspots tend to result insignificantly weaker changes oftransmission properties. This suggests thatcharge transport could play a significant rolefor DNA-repairing deficiency yieldingcarcinogenesis. Their paper was submittedto Phys. Rev. Lett. for publication.4. M.-C. Wu, Z. R. Struzik, E. Watanabe, Y.Yamamoto, and C.-K. Hu studied thetemporal evolution for the phase histogramof ECG during human ventricularfibrillation. They found that some type ofphase distribution is fatal. Their result wasfirst published at AIP ConferenceProceedings 922, (AIP, New York, 2007)edited by M. Tacano, Y. Yamamoto, and M.Nakao, pp. 573-576. A paper to besubmitted to a journal is under preparation.V. PublicationFrom January to August 2007, our FG has14 papers published or accepted by SCIjournals and 3 papers published at a AIPConference Proceedings The SCI journalpapers include 5 in Physical Review E, 2 in J.Statistical Physics, 1 in J. Chemical Physics, 1in Biophysical J., 1 in J. ComputationalCemistry, 1 in Physica A, 1 in Chaos, SolitonsHighlights of Programs -›› 112

and Fractals, 1 in Int. J. Mod. Phys. B, and 1in J. of the Korean Physical Society. The list ofthese papers is showed below and the pdf filesof these papers can be found athttp://phys.cts.nthu.edu.tw/research/focus_group.php?Sn=38. Our FG has sent 15 papers tojournals for publication.Papers published or accepted for publication[1] Cheng-Hsiao Lin, Yan-Chr Tsai and Chin-Kun Hu, Wrapping conformations of apolymer on a curved surface, Phys. Rev. E75, 031903 (2007).[2] N. Sh. Izmailian, Vl. V. Papoyan, V. B.Priezzhev and Chin-Kun Hu, Selforganizingbehavior in a lattice model forco-evolution of virus and immune system,Phys. Rev. E 75, 041104 (2007).[3] Bidhan Chandra Bag and Chin-Kun Hu,Escape through an unstable limit cycledriven by multiplicative colored non-Gaussian, Phys. Rev. E 75, 042101 (2007).[4] Yevgeni Sh. Mamasakhlisov, ShuraHayryan, V. F. Morozov and Chin-Kun Hu,RNA folding in the presence ofcounterions, Phys. Rev. E 75, 061907(2007).[5] N. Sh. Izmailian and C.-K. Hu, Finite-sizeeffects for the Ising model on the helicaltori, Phys. Rev. E 76, in press (2007).[6] Yevgeni Sh. Mamasakhlisov, ShuraHayryan and Chin-Kun Hu, Randomsequences with power-law correlationsexhibit, J. Chem. Phys. 126, 145103(2007).[7] Mai Suan Li, Maksim Kouza and Chin-Kun Hu, Refolding upon Force Quenchand Pathways of Mechanical and ThermalUnfolding of Ubiquitin, Biophysical J. 92,547-561 (2007).[8] Shu-Chiuan Chang, Lung-Chi Chen andWei-Shih Yang, Spanning Trees on theSierpinski Gasket, J. Statistical Phys. 126,649-667 (2007).[9] David B. Saakian, A New Method for theSolution of Models of BiologicalEvolution: Derivation of Exact Steady-State Distributions, J. Statistical Phys. 128,781-798 (2007).[10] Shu-Chiuan Chang and R. Shrock, Zerosof the Potts Model Partition Function inthe Large-q Limit, Int. J. Mod. Phys. B21, 979-994 (2007).[11] Ruben G. Ghulghazaryan, Shura Hayryanand Chin-Kun Hu, Efficient Combinationof Wang-Landau and Transition MatrixMonte Carlo Methods for ProteinSimulations, J Comput Chem 28, 715-726, (2007).[12] Chuan-Ji Fu, Bing-Hong Wang, Chuan-Yang Yin, Tao Zhou, Bo Hu, Kun Gao,P.M. Hui, Chin-Kun Hu, Analyticalstudies on a modified NagelSchreckenberg model with the Fukui-Ishibashi acceleration rule, Chaos,Solitons and Fractals 31, 772-776 (2007).[13] Ming-Chya Wu, Phase correlation offoreign exchange time series, Physica A375, 633-642 (2007).[14] Ming-Chya Wu, Phase StatisticsApproach to Time Series Analysis,Journal of the Korean Physical Society,50, 304-312 (2007).[15] M.-C. Wu, Z. R. Struzik, E. Watanabe, Y.Yamamoto, and C.-K. Hu, Temporalevolution for the phase histogram of ECGduring human ventricular fibrillation, AIPConference Proceedings 922 (AIP, NewYork, 2007) edited by M. Tacano, Y.Yamamoto, and M. Nakao, pp. 573-576.[16] C.-K. Hu, Quantum and lattice models ofbiological evolution, AIP ConferenceProceedings 922 (AIP, New York, 2007)edited by M. Tacano, Y. Yamamoto, andM. Nakao, pp. 589-594.[17] Y.-C. Hung and C.-K. Hu, Detectingessential nodes in complex networks frommeasured noisy time series, AIPConference Proceedings 922 (AIP, NewYork, 2007) edited by M. Tacano, Y.Yamamoto, and M. Nakao, pp. 603-606.113 ‹‹- Highlights of Programs

Focus Group on Nonlinear Phenomena in Physical andBiological SystemsCoordinator: Sy-Sang Liaw (National Chung Hsing University; email: liaw@phys.nchu.edu.tw)Committee members: Chao-Nien Chen (National Changhua University of Education),Kai-Jung Chi (National Chung Hsing University), Tzyy-Leng Horng (Feng Chia University),Jiunn-Ren Roan (National Chung Hsing University), Ming-Chih Shih (National Chung Hsing University)I. Introductionhe focus group consists of the facultymembers and Ph. D students fromvarious institutes in Taiwan, and two foreigncollaborators. The main theme of the groupfocuses on the non-linear phenomena thatappear in nature, including the biologicalworld. Our activities include regular meetings,workshops, and short visits from or toinstitutes abroad.Current projects under intensifieddiscussion include:1. The mechanism of the Brazil nut effect andits reverse (Granular Physics);2. Biological patterns and stability of theTuring equation (Pattern Formation);3. Statistical behavior of agents in economics(Econophysics).Main tools for the investigation aremathematics and physics. Because of theinterdisciplinary nature of our topics, weconstantly consult with experts fromeconomics and biology departments.II. ActivitiesRegular meeting (I)Nonlinear phenomena seminar Friday:12:00-13:00About 10 to 15 people attend the seminar ateach gathering.Regular meeting (II)Biophysical Journal Club (BJC)Thursday:12:00-13:00This BJC has been well organized andsuccessful in terms of broadness of attendance.The mailing list of BJC continues growing.About 15 to 25 people attend the Club at eachgathering. Details of the BJC can be found athttp://140.120.11.15/vedio/biophysics/Chinese/ournal%20club/activity.htmWorkshopsBiophysics workshop: Life among theformulae of physics, Huisun Forest Station,NaTou, Nov. 2-4, 2007We focus on the biomechaics in thisworkshop. Four prestigious speakers: S. Vogel(Duke Univ.); A. Summers (UC, Irvine); D.Hu (NYU); and S. Gorb (Max-Planck Int.) willgive 2 lectures each in the workshop. Theaudience is expected to about 120 people.ConferencesUnder the support of the focus group, wehave sent seven Ph. D students to attendinternational conferences:• C. Liu and C.H. Hung, Turin, Italy, 6/28-7/1, 2006The The 5 th International Conference onApplications of Physics in FinancialAnalysis. They contributed to theconference by one oral and one posterHighlights of Programs -›› 114

presentations.• R.T. Liu and F.F. Chung, Pohang, Korea,7/12-7/15, 2006The 4 th International Conference onNonlinear Science. They presented twoposters.• R.T. Liu, J.Y. Wang, F.F. Chung, Hangzhouand Jinhua, China, 11/12-15, 2007The 3 rd Cross-strait conference onstatistical physics. They will do either oralor poster presentation.III. International collaborations1. Biological pattern formation: Liaw, Liu,MainiProfessor S.S. Liaw of NCHU, ProfessorP.K. Maini of Oxford, and Dr. R.T. Liu ofNCHU have together worked on the biologicalpattern formation for a few years. One of theirjoint publications has been highlighted byNature magazine in 2006. They are currentlyfinishing up a paper on the oscillatory Turingpatern.2. Sand flow through a vertical pipe: Liaw,Liu, Shih, MatsushitaThe experiment was proposed by Prof.Matsushita of Chuo University during his visitto our group in September, 2005. We set up theexperiment immediately and have observedmany interesting phenomena since then. Weare constructing a model to simulate thedensity flow of the sand in the pipe, and toanalyze its power law.IV. Highlights of Research ResultsThe Brazil nut effect in granular physicshas puzzled physicists for more than 50 years.After two years of intense study, Prof. Liawand his students have come up with amechanism that successfully describes a typeof horizontal segregation phenomenon verysimilar to the Brazil nut effect. They areoptimistic in solving the long-standing puzzlein the coming year. They have completed threepapers for reporting their findings. Prof. Liawhas been invited to present these results inAcademia Sinica and NCTS. Prof. Liaw wasalso invited to give a plenary talk in 12 thSymposium on recent advances inBiophysics(5/23-25, 2007, NIH) on hisprevious work on the leopard's spots, whichwas reported in Research Highlight of Naturemagazine (Aug. 2006).We have found veryinteresting phenomena in the emergingeconophysics using agent based simulation onthe model of the Minority game.Our results onthe minority game have some implications tosystems having self-organization criticality.V. Selected Publications[1] Fei-Fang Chung, Ruey-Tarng Liu, and Sy-Sang Liaw, "Horizontal size segregation ingranular matter", J. Korean Phys. Soc. 50,224 (2007).[2] Fei Fang Chung, Sy-Sang Liaw, and Chia-Yi Ju, "Brazil nut effect in a rectangularplate under horizontal vibration", to bepublished in New Journal of Physics(2007).[3] Chia-Hsiang Hung and Sy-Sang Liaw,"Effective history length of the minoritygame", Physica A382, 129 (2007).[4] S.S. Liaw, C. Liu, and C.H. Hung, "Threephases of the minority game", PhysicaA374, 359(2007).115 ‹‹- Highlights of Programs

Focus Group on Soft-matters, Biophysics andSystems BiologyCoordinator: Pik-Yin Lai (National Central University; email: pylai@phy.ncu.edu.tw),Hoong Chien Lee (National Central University; email: hclee@phy.ncu.edu.tw)Committee members: Cheng-Hung Chang (National Chiao-Tung University & National Center for Theoretical Sciences),Chi-Ming Chen (National Taiwan Normal University), Hsien-Da Huang (National Chiao-Tung University),Hsueh-Fen Juan (National Taiwan University), Chun-Yi David Lu (National Taiwan University),Ann- Pin Tsou (National Yang- Ming University)I. Brief Descriptionn the past year, the focus groups ofSoft-Bio Matters and SystemsBiology have been reformed and combined asone under the new name Soft-matter,Biophysics & Systems Biology (SBSB) focusgroup. The new SBSB focus group is nowbigger and contains participants from evenmore diversified fields, especially with manymore biology background researchers.Academic activities have increasedappreciably, especially for workshops andseminars. In the past year, we have organized anumber of activities to promote collaborationsboth within Taiwan and internationally. Ourpurpose is to encourage the use of theoreticalmeans to investigate the fundamentalprinciples in soft-matter and bio-relatedsciences and aiming at obtaining somequantitative understanding in soft materialsand biological processes with emphasis on themore recent hot topics using systemsapproaches to investigate biological systems.Emphasis is also put on the communicationsand collaborations with experimentalists, asreflected by the fact that some of the activemembers of the focus group areexperimentalists also. In recent years, we haveencouraged strongly on creating actualcollaboration environment between our localmembers and researchers in the Asian-Pacificregions and we are starting to see someconcrete outcomes. The (SB) focus group isrun by a committee of 6 researchers fromvarious institutions which is listed at thebeginning.SBSB focus group also organizes regularand irregularly scheduled seminars,workshops, conferences on soft-matterphysics, biophysics and systems biology heldat various associated institutions. We havebeen organizing the weekly "Soft-Bio MattersSeminar/Journal Club" for more than 4 years,at NCU. This active seminar series has beeninviting local and foreign visiting researcherson various areas of soft-matter and biophysicsand it turns out that various research ideas andactual collaborations are indeed come out asdirect/indirect consequences of this seminarseries. In the past year, some topics are moreemphasized in the areas of DNAconformations, genomic/protenomic analysis,evolution theory, nonequilibrium physics inpulling biomolecular bonds, polyelectrolytes;rheology & pattern formation in complexfluids; excitable bio-systems such as cardiacand neural biophysics; collective motions inactive organisms; membrane biophysics;dynamics on complex and bio networks; Brainphysics; physics of DNA & proteins, etc.II. ActivitiesWe organized a number ofworkshop/schools as well as one internationalscale meetings. We have attracted a number ofyoung and established local researchers, aswell as participants from nearby countries. It isworth to mention that theseworkshop/conferences always attract a goodHighlights of Programs -›› 116

collection of active researchers from variouslocal institutions to participate/organize theseactivities in an active way.1. Biophysics Camp 2006 (NCU) Oct. 21~22,20067. Mini-workshop on Complex Systems 2007(NCU) July 16~19Discussions during the Mini-workshop on ComplexSystems 2007Participants of Biophysics Camp 20062. Miniworkshop on Quantitative Biology(NCU) Dec. 27, 20063. BioPhysics & Soft-Matter Days 2007(Kenting) January 26~28Soft-Matter & Biophysics Days 2007 at Kenting's YOHOresort4. Second Workshop on Systems Biology andBioinformatics (NCU) April 14~155. 2007 Taipei International Workshop for SoftMatter and Biophysics (Taipei) May 20~246. The 18 th Complex Systems Symposium(NCU) June 2~3Student speaker at the 18th Complex SystemsSymposiumIn May, we organized the "2007 TaipeiInternational Workshop for Soft Matter andBiophysics" at Taipei. World renownedphysicists and biophysicists delivered series oflectures in the conferences. Speakers include:Prof. Robert H. Austin (Physics Dept.,Princeton Univ.) Prof. Jacob Kiein (Dept. ofChemistry, Oxford Univ.) Prof. Gerard C. L.Wong (Dept. of Materials Science andEngineering, Univ. of Illinois.) Prof. Sean Ling(Dept. of Physics, Brown Univ.) Prof.Chengde Mao (Dept. of Chemistry, PurdueUniv.) Prof. Meredith Betterton (PhysicsDept., Univ.of Colorado). A large number ofresearchers of different backgroundsparticipate in these workshops. Many of themare already involved with SBSB research andfound this workshop very stimulating. Inaddition, there are many potential futureresearchers and students that were fascinatedby the rapid advances and promising futurepotential in this area. These activities clearlyreflected a strong rise in researchers/students'interest in bio-related theoretical sciences.Biological related theoretical sciences areexpanding in a rapid pace, and it seems that itwill keep on growing in the foreseeable future.Soft-matter physics is the foundation to theunderstanding of the material nature of thesebiological systems. We anticipate that with thesupport of NCTS, SBSB research in Taiwanwould have a very good chance to contributepromising results in these very competitiveareas.117 ‹‹- Highlights of Programs

III. Visitors and InternationalCollaborationsSBSB focus group also supported a numberof foreign visiting scientists aiming atacademic inteflow of ideas and set upcollaborations. We have both short and longtermvisitors, delivering lectures and carryingout collaborations. Foreign visitors in the pastyear include: Dr. Jih-Chiang Tsai(Northwestern U.), Dr. Wan-Chen Lin(University of California, Davis), Prof. QiOuyang (Peking U.), Dr. Armen E.Allahverdyan(Yerevan Physics Institute), Prof.Kuan Wang(National Institutes of Health),Prof. David B Saakian(Yerevan PhysicsInstitute), Prof. Jenifer Thewalt (Simon FraserU.), Prof. Hai Jun Zhou (Chinese Academy ofSciences, Beijing), Prof. Hyoung Jin Choi(Inha U.), Dr. Wei-Yuan Yang(Harvard U.),Prof. Dongchuan Yu (Qingdao U.).In the past year, we have been speciallyfocused on attracting/promoting students toenter into our field by organizing theBiophysics Camp, the response was verypositive. The format of the 18 th ComplexSystems Symposium was also modified tobecome a symposium with speakers consistedof solely graduate students. In this two-daysymposium, graduate students from variousinstitutions reported their concrete researchresults. The best two speakers were awardedwith best presentation awards. Students foundthis to be very stimulating and the positivecompetition among the students transformedinto an enthusiastic atmosphere. We shallcontinue such kind of activity in the future.IV. Selected Publications[1] Hsuan-Yi Chen and Kwan-tai Leung,Rotating states of self-propelling particlesin two dimensions, Phys. Rev. E73, 056107(2006).[2] Jia-Yuan Wu, and Hsuan-Yi Chen,Membrane-adhesion-induced phaseseparation of two species of junctions,Phys. Rev. E73, 011914 (2006).[3] Pik-Yin Lai, L.-C. Jia, and C. K. Chan,Growth of Cortical Neuronal Networks invitro: modeling and analysis, Phys. Rev.E.73, 051906-1~9 (2006). Also selected inVirtual Journal of Biological PhysicsResearch 11, issue 10 (2006).[4] J.R. Roan, Soft Nanopolyhedra as a Routeto Multivalent Nanoparticles, Phys. Rev.Lett. 96, 248301 (2006). Also reported inPhys. Rev. Focus 17, story 22, June, 2006.[5] C. T. Shih, Characteristic length scale ofelectric transport properties of genomes,Phys. Rev. E 74, 010903 (2006).[6] D.-w. Huang, Ramp-induced transitions intraffic dynamics, Phys. Rev. E73, 016123(2006).[7] C.-H. Cheng, Boundary condition ofpolyelectrolyte adsorption, Phys. Rev. E73,012801 (2006).[8] J. Henriksen, A. C. Rowat, E. Brief, Y. W.Hsueh, J. L. Thewalt, M. J. Zuckermann,and J. H. Ipsen, Universal Behavior ofMembranes with Sterols, Biophys. J. 90,1639 (2006).[9] Zi-Hao Wang, Ming-Hua Chang, Jenq-WeiYang, Jyh-Jang Sun, H.C. Lee and Bai-Chuang Shyu, Layer IV of the primarysomatosensory cortex has the highestcomplexity under anesthesia and corticalcomplexity is modulated by specificthalamic inputs, Brain Research 1082(2006) 102-114.[10] Dominique Chu, Jonathan Rowe, andHoong-Chien Lee, Evaluation of theCurrent Models for the Evolution ofBacterial DNA Uptake Signal Sequences,J. of Theoretical Biology 238 (2006) 157-166.[11] S. Bastrukov and Pik-Yin Lai, On theSurface Gyromagnetic Plasmons in ametal sphere, Surf. Rev. & Lett. 13(2006).[12] S. Bastrukov, Pik-Yin Lai, D. Podgainyand I. Molodtsova, Optical Response ofmagnetically aligned nematic soft matterby transverse nemato-magnetic waves, J.of Mag. & Mag. Materials (2006).Highlights of Programs -›› 118

[13] C.H. Chen and Hsuan-Yi Chen, Finitesizedomains in membranes with activetwo-state inclusions, Phys. Rev. E74,051917 (2006).[14] L. C. Jia, C. R. Han, C. H. Chang, M. T.Tsai, Y. S. Chou, Pik-Yin Lai, and C. K.Chan, Synchronized Bursting induced bynetwork connectivity in cortical neuronalcultures, J. Korean Phys. (invited article),50, p.207~218 (2007)[15] H.J. Lin, H. Y. Chen, Y.J. Shen, and H. K.Tsao, Bell's Expression and theGeneralized Garg Form for ForcedDissociation of a Biomolecular Complex,Phys. Rev. Lett. 98, 088304 (2007).[16] Y. W. Hsueh et. al., Ergosterol in POPCMembranes: Physical Properties andComparison with Structurally SimilarSterols, Biophys. Journal 92, 1606 (2007).[17] W. C. Hung, M.T.Lee, and F.Y. Chen, TheCondensing Effect of Cholesterol in LipidBilayers, Biophys. J. 92, 3960 (2007)[18] F. T. Chien, S. G. Lin, Pik-Yin Lai and C.K. Chan, Observations of Two forms ofConformations in the Re-entrantCondensation of DNA, Phys. Rev. E75,041922 (2007).[19] O.I. Kanakov, G.V. Osipov, C. K. Chan,and J. Kurths, Cluster synchronizationand spatio-temporal dynamics innetworks of oscillatory and excitable Luo-Rudy cells, Chaos 17, 015111 (2007).[20] D. W. Huang, Bi-directional ant traffic ontrails, International Journal of ModernPhysics C 18 , p.407 (2007).[21] D. W. Huang, Phase diagram of a trafficroundabout, Physica A 383, p.603 (2007).[22] Y.-S. Tsai and C.-M. Chen, Drivenpolymer transport through a nanoporecontrolled by a rotating electric field: Offlatticecomputer simulations, J. Chem.Phys., 126, 14491 (2007).[23] D.-M. Ou, C.-C. Chen, and C.-M. Chen,Contact-induced structure transformationin transmembrane prion propagation,Biophys. J., 92, 2704 (2007).* The above publications are direct or indirect outcomes ofthe activities organized by our focus group. However, notallof these publications have shown affiliation with NCTS.119 ‹‹- Highlights of Programs

Highlights of ProgramsCondensed Matter PhysicsFocus Group on Computational Materials ResearchCoordinator: Tsan-Chuen Leung (National Chung Cheng University; email: tcleung@phy.ccu.edu.tw)Committee members: Chun-Ming Chang (National Dong Hwa University), Ching Cheng (National Cheng Kung University),Guang-Yu Guo (National Taiwan University), Ming-Hsien Lee (Tamkang University),Shiow-Fon Tsay (National Sun Yat-sen University)I. Introductionhe chief purpose of this group is toenhance the domestic researchcapacity in computational material scienceespecially quantum mechanics-based ab initioelectronic structure calculations and moleculardynamics simulations, through promotingexchange and collaboration among localmembers as well as between Taiwan andforeign members, and also through attractingmore young researchers into this field. To thisend, like previous years, we have organized abinitio methods study group meeting, minischoolswith leading international scientists asmain lecturers, and also program-wide annualconference. Furthermore, to attract youngerresearchers as well as experienced ones to thefield of CMR and also promote awareness ofthe important role in the modern scientificresearch played by the computation usingpresent-day computers, we have alsoorganized spring school (introductory level)and summer school (advanced level) on firstprinciplescomputational materials research.We have encouraged members especiallyyoung ones to attend relevant internationalconferences, workshops and schools.Specifically, we supported Ru-Fen Liu(postdoc. at NCKU), C. H. Cho (Ph. D. studentat CCU), and C. H. Yao (Ph. D. student atNDHU) to attend international school. We alsosupported C. Y. Ren (NKNU) and B. R. Wu(CGU) to visit NCTS this summer in order topromote the collaboration among localmembers. The gatherings of this kind haveprovided an essential channel for fruitfuldiscussions among members of thecommunity, and in particular, benefit ourpostgraduate students and young postdoctoralfellows tremendously.The CMR focus group consists of 42members (29 faculties and 13 Ph. D. studentsand postdocs). It is run by a committee fromvarious institutions. The missions of thecommittee are to allocate the budget, to initiateresearch activities, to invite the long-term andshort-term visitors and to recommendcandidates (Ph. D. student or junior scientist)to attend international school, conference, orworkshop with the financial support ofCMRFG.II. Activities1. Mini-School on Time-Dependent DensityFunctional Theory: Foundations andApplicationsHighlights of Programs -›› 120

The ground-state based nature of theconventional Density Functional Theory(DFT) method has difficulties in tacklingelectronic excitations. An alternative methodwhich is comparatively simpler in formalism isthe time-dependent (TD) DFT. TDDFT hasgreat success in describing excitations in finitesystems such as nanoclusters. The Mini-School on Time-Dependent DensityFunctional Theory: Foundations andApplications, organized by G. Y. Guo (NTU),is held in National Taiwan University inMarch 16-17, 2007. Two of the leadingfigures in the field, namely, Prof. Eberhard K.U. Gross (Berlin Free Univ.) and Prof. Shih-IChu (Univ. of Kansas and National TaiwanUniv.), gave five lectures on the foundations,recent new developments, and applications ofTDDFT.2. Mini-School on Tight Binding Simulationon NanomaterialsThe ability to perform reliable simulationsof molecules and solids systems withthousands of atoms has enormous payoffs inmany fields. The Mini-School on TightBinding Simulation on Nanomaterials,organized by T. C. Leung (CCU), is held inNCTS in June 22-23, 2007. Prof. C. W. Wangfrom Ames Lab. (USDOE) gave four lecturesto review the tight binding theory, formulismand the development of tight bindingpotentials for molecular simulation ofmaterials. Application of tight bindingmolecular dynamics to the studies ofnanoclusters, carbon nanotubes, and surfacebasednanostructures were discussed.3. The 7th Workshop on First-PrinciplesComputational Materials PhysicsThe 7th Workshop on First-PrinciplesComputational Materials Physics, organizedby S. F. Tsay (NSYSU), was held on Jan. 29-31, 2007 in National Sun Yat-sen University.The aim of this conference is to promoteinteraction and collaboration among localphysicists. The Program Committee wouldalso like to take this opportunity to hear aboutinterests of the community in order to planfuture activities at the Center. Like previousyears, all participants including PhD studentsand young postdocs, were encouraged to givea talk in this workshop. The workshop willcover the subjects related to our program suchas description of physics and computationalmethods or report of results. The scientificprogram consisted of four 40-50-minuteslectures, eight 30-minutes research reports andten 20-minutes talks by student.4. Spring school on First-PrinciplesComputational Materials Research -Introductory LevelThe spring school on first-principlescomputational materials research-introductorylevel, lectured by T. C. Leung (CCU), is heldin National Center for High-PerformanceComputing. The purpose of this school is tooffer an introduction to the fundamentals of abinitio density functional theory, ofpseudopotentials, and large scale calculations,as well as a practical hands-on training foryoung students and non-specialists. Theresponse from both young students and nonspecialistresearchers were very positive, therewere more than hundred participants in thisspring school.5. Summer School on First-PrinciplesComputational Materials Research –Advanced LevelThe summer school on first-principlescomputational materials research – advancedlevel, organized by C. Cheng (NCKU) and T.C. Leung (CCU), is held in NCTS. Thepurpose of this school is to offer the audiencesa deeper understanding on the fundamentals ofab initio density functional theory, ofpseudopotentials, and large scale calculations.Particular emphasis will be laid on a thoroughdiscussion of the problems that can be solveddirectly with the basic code. There were morethan fifty participants in this summer school.6. Asian Workshop on First-PrinciplesElectronic Structure CalculationsThe 9 th Asian Workshop on First-PrinciplesElectronic Structure Calculations was held inKorea, Nov. 1 – 3, 2006. This is a big event inthe Asian community of ab initio research.This series of workshop is initiated at 1998 byProf. K. Terakura of Japan and K. J. Chang of121 ‹‹- Highlights of Programs

Korea, more than 100 scientists from the Asiancountries such as China, Hong Kong, Japan,Korea, India, Singapore, and Taiwan, and alsofour to five leading experts from Europe andUSA participate in this workshop. The 4 thAsian Workshop was held in National TaiwanUniversity in 2001, the 7 th Asian Workshopwas held in Tamkang University in 2004, andthe 11 th Asian Workshop will be held inNational Sun Yat-sen University. Eighteenmembers of CMRFG participate the 9 th AsianWorkshop last year. The next meeting will beheld in Japan and we will continue beingactive in this Asian community of ab initioresearch.7. OpenMx Study Group MeetingIt is well known that the computing time ofcurrently popular electronic structure methodsbased on Density Functional Theory scale likeN 2-3 , with N being the number of atoms in thesimulation cell. In the last few years, mucheffort has been devoted to overcome thisproblem, and a number of methods have beendeveloped with "order – N "[O(N)] scaling,i.e., whose computational cost scales onlylinearly with the number of atoms. One of thesuccessful order N ab initio computing code isOpenMx (Open source package for Materialexplorer) developed by Dr. Taisuke Ozakifrom National Institute of Advanced IndustrialScience and Technology in Japan. In order tofamiliar with the principles used in theprogram and how they are implemented so thatthe program can be properly applied to thesystems we want to study, several study groupmeeting on OpenMx was organized by T. C.Leung (CCU) and held in NCTS. The keymembers involved in this project are C. S.Hsue (NTHU), Y. T. Lu (NCKU), W. C. Kuo(NSYSU), T. L. Li (NCYU), T. C. Leung(CCU), Y. C. Hsu (NCKU), S. F. Tsay(NSYSU), G. Y. Guo (NTU), S. H. Chiou(ITRI), C. Y. Ren (NKNU), and B. R. Wu(CGU).8. Excited State Study Group MeetingThe conventional DFT method fails to giveaccurate excitation properties, e.g., band gaps,excitonic binding energies, of solids. The GWmethod has been successfully used to predictelectronic properties of a variety of differentsystems, ranging from bulk materials tosurfaces, nanotubes, and molecules, whereasthe linear optical response is routinely studiedby solving the Bethe-Salpeter Equation (BSE)with comparable success. ABINIT is apackage whose main program allows one tostudy the excited states using the GWapproximation. On the other hand, the EXC isan exciton code which uses the output ofABINIT to calculate the dielectric and opticalproperties for a large variety of systems bysolving the Bethe-Salpeter equation. In orderto familiar with the principles used in theprogram and how they are implemented so thatthe program can be properly applied to thesystems we want to study, Exited State StudyGroup Meeting was organized by G. Y. Guo(NTU) and held in NTU. The key membersinvolved in this project are G. Y. Guo (NTU),T. C. Leung (CCU), Y. J. Tsai (CCU), H. C.Hsueh (TKU) , M. Hayashi (CCMS), C. K.Yang (CGU), H. T. Jeng (AS), and B. R. Wu(CGU).III. Collaborative ActivitiesThe examples of these collaborations betweenCMRFG members are listed as follows:1. C. M. Chang (NDHU), C. Cheng (NCKU)and C. M. Wei (AS) on the Quantum MonteCarlo simulation on nanomaterials.2. H. T. Jeng (AS) and C. S. Hsue (NTHU) onthe Orbital Ordering in transition-metaloxides.3. C. Y. Ren (NKNU), S. F. Tsay (NSYSU)and F. C. Chuang (NSYSU) on theelectronic structure of Au/Si(111) (5x2).4. B. R. Wu (CGU) and T. C. Leung (CCU) onthe electronic and optical properties ofribbon under external electric field.5. G. Y. Guo (NTU), T. C. Leung (CCU) andH. C. Hsueh (TKU) on the ab initio studyon excited state of nanomaterials.International collaborations are listed asfollows:1. K. Terakura (Japan) and G. Y. Guo (NTU)Highlights of Programs -›› 122

on the static dielectric response of BNnanotubes from ab initio finite electric fieldcalculations,2. C. T. Chan (Hong Kong) and T. C. Leung(CCU) on the field emission properties ofnanomaterials.3. M. Y. Chou (USA) and C. M. Wei (AS) onthe quantum well states in metal thin films.4. Steven G. Louie (USA) and H. C. Hsueh(TKU) on the quasiparticle excitations innanomaterials.IV. Highlights of Research Results1. Current and strain-induced spinpolarization in InGaN/GaN superlatticesMain team members:G. Y. Guo (NTU) and Y. F. Chen (NTU,experimentalist)It has been proposed theoretically that atransverse spin current, the so called spin Hallcurrent, can be generated in strongly spin-orbitcoupling systems by external electric field.We have investigated the current-induced spinpolarization in InGaN/GaN superlattices. It isfound that the degree of polarization changessign as the direction of the current flow isreversed. The strain-induced spin Hall effectdiscovered here paves an alternative way forthe creation of spin polarized current, whichshould be useful for the realization of thefuture applications in spintronics.H. J. Chang, T. W. Chen, J. W. Chen, W. C.Hong, W. C. Tsai, Y. F. Chen, and G. Y. Guo,Phys. Rev. Lett. 98, 239902 (2007).2. Orbital Ordering and Jahn-TellerDistortion in Perovskite RuthenateSrRuO 3Main team members:H. T. Jeng (AS) and C. S. Hsue (NTHU)Orbital, charge, spin, and lattice degrees offreedom play important roles in the electronic,magnetic, and transport properties oftransition-metal oxides. It was proposed thatorbital ordering is closely related to magneticand crystallographic lattices in perovskitemanganites such as La 1-x Ca x MnO 3 in the lowtemperature insulating charge ordered phase.We have investigated the electronic structuresof SrRuO 3 in the distorted orthorhombicstructure using LDA+U. The obtained bandenergies agree well with those fromphotoemission and X-ray absorptionspectroscopy. Our finding unravels the natureof the orbital ordering, the close connection tothe JT distortions, and the importance of theon-site correlation U in the relatively extendedRu 4d orbitals.H. T. Jeng, S. H. Lin, C. S. Hsue, Phys. Rev.Lett. 97, 67002, (2006)3. Highly Spin-polarized field emissioninduced by quantum size effects inultathin films of Fe on W(001)Main members:T. C. Leung (CCU) and C. T. Chan (HongKong)Nanostructured systems have enhancedeffects due to the confinement of quantizedstates, and, for the particular case of ultrathinsupported films, many amazing structural andelectronic properties have been discovered.Although tungsten is the metal of choice foremitter tips, it does not produce spin-polarizedfield emission currents. We use densityfunctional calculations to study the spinpolarizedfield emission from pseudomorphicFe ultathin films on W(001). We found thatnearly completely spin-polarized fieldemission currents can be realized in two andfour Fe layers on W(001) and that thesesystems have the additional advantages ofthermal stability and low work functions. Thethickness dependent field emission propertiesare traced to spin-polarized quantum well andsurface resonance states localized in the Felayers.Bin Li, T. C. Leung, C. T. Chan, Phys. Rev.Lett. 97, 87201 (2006).Remark: For detail publications, please see the webpagehttp://phys.cts.nthu.edu.tw/research/focus_group.php123 ‹‹- Highlights of Programs

Focus Group on Low-Dimensional Systems and NanostructuresCoordinator: Jang-Yu Hsu (National Cheng Kung University; email: jyhsu@phys.ncku.edu.tw)Committee members: De-Hone Lin (National Sun Yat-sen University), Min-Fa Lin (National Cheng Kung University),Chi-Tin Shih (Tung Hai University), Yan-Chr Tsai (National Chung Cheng University),Chih-Kai Yang (Chang Gung University)I. Brief Descriptionhe nanostructure and lowdimensionality presents peculiarphysics uncommon to the classical or theinfinite-sized quantum system. The beautifulfullerene is a zero dimensional system, thecarbon nanotube, a one dimensional system,and the graphene, a two dimensional system.The opportunities for scientific discovery andfor technology breakthrough therefore abound.The nanoparticles or nanostructures areintermediate between atomic and macroscopicscales representing an emerging field ofintense research, known as the mesoscopicphysics. The nonlinear many body effecthowever, manifests itself in rich phenomenaand present many challenges, both theoreticaland experimental to the researchers in thefield.This focus group formed in year 2004 is theyoungest among the NCTS siblings, andrepresents a new, evolving and novel directionof research. Its main purpose is to promotecollaborations among faculty members,postdoctors, graduate students as to integratethe available research methods, resources andthe manpower. In particular, this group hashelped neighboring universities to organizeworkshops and summer schools, to finance theforeign trips and invited speakers, and tofrequent the summer resident scholars of theyoung, the diligent and the innovative. Theresearch interest while diverse may becategorized into the following: carbon related,nanoparticle, molecular device, and bio andadvanced concepts.II. ActivitiesThe focus group has, for serving ourmembers and young scholars alike, organizedworkshops and tutorial schools by invitingdomestic and foreign scholars to review theexperimental and theoretical progress andprospect in nanoscience. As part of the effortto achieve the center of excellence for NCTS,summer residency of theoreticians is stronglyencouraged. Moreover, NCKU has earmarked100% matching fund to promote the NCTSactivities and to, in additional funding,promote the neighboring institutions foracademic excellence.In the four seasons, we organize the majorworkshops at various universities with theparticipants numbered around fifty peopleeach time. The availability of high speed bullettrain will further enhance the collaboration andpartnership of scientists between the south andthe north Taiwan, and will increase the foreignscholar visits. The summer residence atNCTS-south has 4 scientists and called ourattention to propose adding shower room anddormitory accommodation. We haveimplemented the video conferencing, eJournalclub web pages, and the database for videopresentations and power point files. Eachworkshop has compiled proceedings ofabstracts to document members' recentresearch results and to encouragecollaborations and innovations.Miniworkshops are organized in the hotsummer days. Foreign trips for postdocs andgraduate students have been financed throughNCTS and NCKU funding. Weekly luncheonmeetings were held during the schoolsemesters with participants mainly withinHighlights of Programs -›› 124

Tainan area as understandably limited by timeand effort for long distance travel, but theinvited speakers of the followed seminar docome without. Short term foreign visitors areinvited in conjunction with the AutumnWorkshop as it is the largest planned.III. Visitors and InternationalCollaborationsForeign Visitors:Professor Zhao Jijun from Dalin Universityof Technology in China, is an expert of firstprinciple calculations on nanostructures.During his visit, he provided very instructivelectures on genetic algorithms, goldnanoparticles and structural, electronic,vibrational and magnetic properties offullerene and variants. Under our invitation tocome in September is Dr. Stephan Roche ofFrance, an author of the recent review articlein Review of Modern Physics, 79, 677 (2007)(56 pages) on 'Electronic and transportproperties of nanotubes'. We have alsoextended our invitation to Professor WeitaoYang, the Philip Handler Professor ofChemistry at Duke University, with expertisein quantum chemistry, DFT and biomolecules.Domestic Visitors and Summer Residency:By the joining effort with Professor Y. C.Hsue, many domestic speakers were invited tothe Ph. D. student seminars. The summerresidency we had three scholars in year 2006:Prof. C. P. Chang, Prof. C. H. Lin and Prof. R.B. Chen and five scholars in year 2007: Prof.C. P. Chang, Prof. C. H. Lin and Prof. R. B.Chen, Prof. Shih-Jye Sun. Prof. Chang workedon electronic properties of the AA- and ABCstackedfew-layer graphites in the presence ofan electric field, perpendicular to the layersthrough the tight-binding method. Prof. C. H.Lin investigated the wrapping conformationsof a polymer on the nanoparticle surface.Under the assumption of invariant length foreach polymer segment, he obtained a set ofanalytic equations describing the conformationat the minimum free energy. Prof. R. B. Chenstudied energy loss spectra of finite carbonnanotubes. The sp 2 tight-binding model and thegradient approximation are, respectively, usedto calculate electronic states and energy lossspectra. Prof. Shih-Jye Sun will study theadsorption of gas molecules by CNT and theelectrical conductivity.International Conference Participation:By the support of NCTS, Prof. R. B. Chenattended the 16 th International Conference onElectronic Properties of Two-DimensionalSystems in Albuquerque, New Mexico in 2005and Prof Jung F. C. of NSYSU visited Chinain 2007. With the matching fund from NCKU,C. W. Lo and J. Y. Hsu will attend theCCP2007.IV. Highlights of Research ResultsCarbon related:(M. F. Lin) A carbon nanotube (CNT) canexhibit interesting excitation properties, sincethe linear and angular momenta of electronsare conserved on a cylindrical surface. TheSlater-Koster tight-binding model and therandom phase approximation were,respectively, used to study the magneto bandstructures and electronic excitations. Theexcitation spectra strongly depend on themagnitude and the direction of magnetic field,the transferred momentum, the temperature,the nanotube geometry, and the Zeemansplitting. The scattering rate of electrons in thenanotube and graphene was studied. Thelowest two conduction bands in moderate-gapCNTs have the vanishing decay rates owing tothe absence of low-frequency deexcitationchannels. The decay rate of the metallic CNTs,sensitive to the wavevector, has a lineartemperature dependency. The decay rate of theband-edge state is faster as the nanotube radiusincreases. The increased carrier densitysignificantly enhances the intraband lossspectrum and thus the decay rate. As to otherstates, the decay rate under the negative energytransfer is comparable to those under thepositive energy transfer. (C. Y. Yang) Theboron-nitrate nanotube as a "nano-cable",shielding and protecting materials fromoutside interference was examined.125 ‹‹- Highlights of Programs

Nanoparticle:(C. Y. Yang) Ab initio calculations wereemployed to study the physical properties of avariety of nano-scale materials. Of particularinterest was using the fullerene C 60 moleculesto store hydrogen molecules. (F. C. Chuang) Agenetic algorithm was developed to search forthe lowest energy surface structure. Thesestructures were further optimized using firstprinciplecalculations. Several high-indexsurfaces [e.g. Si(105), Si(114), Si(337), andSi(103)] were successfully identified. (J. Y.Hsu) The global minimum energy state ofnanoparticle structure is an NP hard problem.As the number of particles goes up, theproblem becomes intractable andunreasonable, since the neighboring solutionsscale as a super-polynomial function.Adopting a coarse grain (CG) scheme, bothGA and SA were speeded up by the divideand-conquerstrategy, and the calculation isfurther expedited by the local evaluation anddeterministic search (ES) that improves thealgorithm from the diffusive to a deterministicprocess. The proof of principle wasdemonstrated by the fullerene structure withuse of the Tersoff potential.Molecular device:(M. H. Tsai) Conduction through amolecular junction and the growth rate of aGaN nanorod faster than that of the film werestudied theoretically from the first principles.Comparing with the experimental data showsgood quantitative agreement. Our firstprinciplescalculation for the electronicstructures of nm-scale [0001] GaN filmsshows that the internal electric fields and theband tilt of these films are in oppositedirection to those predicted by the genericpolarization of Bernardini, Fiorentini andVanderbilt (P BFV ). Additionally, it is determinedthat an intrinsic self-regulated charge transferacross the film limits the electrostatic potentialdifference across the film, which renders thelocal conduction band energy minimum (at theGa-terminated surface) approximately equal tothe local valence band energy maximum (atthe N-terminated surface). This finding castdoubt on the popular use of P BFV to address theissue of polarity in III-V nitridesemiconductors. (F.C. Chuang) Motivated bythe STM experiments of Ma et al., Science2003, 299, 1874, a combined GA-DFTprocedure to search for the structure of [110]silicon nanowires (SiNWs) up to 60 atoms perunit cell were investigated and reported inNano Letters. (C. Y. Yang) Transportproperties were studied for systems withnanotubes or molecules connected betweentwo electrodes, and with magnetic impuritiesencapsulated or doped for spin transport as inthe spintronics.Bio and advanced concepts:(C. T. Shih) Transport property of p53 geneis studied by a tight-binding model. Thechange of the transmission coefficient isevaluated for all possible point mutations ofp53. On the average, the mutations found inthe tumor tissues reduce the transmissioncoefficients. The result provides anexplanation on how the cancerous mutationsfend off the DNA-repairing mechanism andcause cancers. (D. H. Lin) The Friedel theoremfor the relativistic spin-1/2 system and theconnections among the Friedel sum, Levinsontheorem, and the Atiyah-Singer (AS) indexwere derived. Since the AS index is importantin studying the relations among the invariantsin modern quantum field theory and stringtheory, the present result provides an avenue todiscover new invariant. It is important instudying the 2D graphene system the structureof neutron star, and the application incontrolling a spin bus - a controllable couplerof many qubits.V. PublicationSince the NCTS funding to supportindividual researcher makes an epsilon impacton his/er pocket book in general, it isunderstandable that few of the publishedpapers acknowledged NCTS financial support.The funding for workshop, trip, and summerresidency however will in the long runenhance greatly the collaboration, and willadvance the innovative research as anticipated.The short term gain while is less pronounced,Highlights of Programs -›› 126

NCTS funding will result in the long termbenefit as hereby acknowledged to be moneywell spent. In the past 3 years, more than 50SCI papers were published by the members ofthis group. For detail publications, please seethe webpage http://phys.cts.nthu.edu.tw/research/focus_group.phpVI. One Picture Is Worth TenThousand WordsFig. 3. (a) The Coulomb decay rates of narrow-gap CNsfor the first conduction bands. (b) Those associatedwith positive decay energies and (c) correspond tothe interband c➝v decay.Fig. 1. The inelastic scattering rates of the (5,5) nanotube.They are calculated for the low energy states atT=300 K. Also shown in the inset are those of theconduction-band states from the intrabandexcitations.Fig. 4. The Energy Surface and Dirac Cone at K point ofGrapheneFig. 2. The Coulomb decay rates of moderate-gap CNs forthe first conduction bands. Also shown in the insetare those associated with positive decay energies.127 ‹‹- Highlights of Programs

Focus Group on Mesoscopic and Spin PhysicsCoordinators: Chon-Saar Chu (National Chiao Tung University; email: cschu@cc.nctu.edu.tw )Chung-Hou Chung (National Chiao Tung University; email:chung@mail.nctu.edu.tw)Committee members:Cheng-Hung Chang (National Chiao Tung University and National Center for Theoretical, Science),Yu-Chang Chen (National Chiao Tung University), Shun-Jen Cheng (National Chiao Tung University),Hsiu-Hau Lin (National Tsing Hua University), Juhn-Jong Lin (National Chiao Tung University)I. Brief Descriptionoals:To understand and discover interestingnew phenomena on electronic and spintransport in nanostructures.Research topics:• Electronic transport in semiconductornanostructures. Topics include: quantumphase transition and non-equilibriumtransport in quantum dots associated withKondo effect (C.H. Chung), dissipation andnoise in nano-juction devices (Y.C. Chen andC.H. Chung), dephasing and decoherence indisordered nano-wires/nano-junctions (J.J.Lin).• Spintronics in nanostructures. Topicsinclude: novel magnetic properties in dilutedmagnetic semiconductor (H.H. Lin), spintransport and spin Hall effect in Rashba-type2-D electron gas (2DEG) (C.S. Chu and C.H.Chang), spin-characteristic charged excitonsin self-assembled quantum dots (S.J. Cheng).• Strongly correlated effects innanostructures. Topics include: edge statesand magnetic properties of carbon nanotubes(H.H. Lin), quantum criticality in coupledquantum dots and in cold atoms (C.H.Chung).II. ActivitiesInternational Workshop on Mesoscopic andSpin Physics, NCTU, Jan., 2007:C.S. Chu and C.H. Chang have benefitedfrom the discussions with Prof. RolandWinkler in detail about the effects of gate-biason the local chemical potential. This can beimplemented in their future consideration ofgate-controlled spin dynamics. Two graduatestudents: one Ph.D. student, L.Y. Wang, andthe other master student, K.Y. Chen presentedtheir work to Prof. E.I. Rashba (Harvard), andseparately, to Prof. S.Q. Shen (U. of Hong-Kong). These two students had benefited fromtheir comments and suggestions. C.H. Chungand the invited speaker Walter Hofstetter (U.of Frankfurt) discussed their researchcollaboration in quantum dots and Kondoeffect.International Workshop on Disorder andInteractions in Low Dimensions, June, 2007Many of our FG members and PhDstudents had benefited a lot from discussionswith invited speakers S. V. Kravchenko(Northeast U.), E. Abrahams (Rutgers U.) andDobrosavljevic (NHMFL, Florida State U.) ontheir common research interests on 2D metalinsulatortransitions, disordered systems inlow-dimensional materials and transport inKondo dots. The discussions inspired newideas along these lines. PhD and Materstudents also got trainings from some of thebroader overview talks in the workshop.Seminars and regular discussions:We have invited many local experts andforeign visitors to give seminar talks in NCTSto discuss our research interest. The goals areto develop new ideas, to encourage newcollaborations, to educate students/postdocsand to invite people from institutions withrelatively limited resources to participate. SuchHighlights of Programs -›› 128

examples include:• New projects/ ideas were developed: (i)among J.J. Lin (experimentalist) C.H. Chungand Chi-Tong Chen (Academia Sinica) onthe transport through quantum dots coupledto nanowires. (ii) between J.J. Lin'sexperimental group and C.H. Chung onKondo effect in transport through nanowires.The recent experimental results done byLin's group can be explained very well bythe 2-impurity Kondo model. (iii) amongC.S. Chu, Malshukov, H.H. Lin and C.H.Chang in the spin Hall effect in Rashba-type2DEG. (iv) between S.J. Cheng and Wei-Tong Sheng on excitons in semiconductors..(iv) between H.H. Lin and Horng-TayCheng (Academia Sinica) on magnetism incarbon- nanotubes. They have very fruitfulresults.• Education for students/postdocs/youngfaculty: Prof. Y.C. Lee (SUNY, Buffalo) hasvisited NCTS from March till July. Duringthis period, he has given a series of lectureson topics including Bose-Einsteincondensation, High Tc superconductivity,and a basic investigation of the spinnonconservation in spin-orbit interaction.Prof. B.L. Young (NCTU) and T.F. Jiang(NCTU) had discussions with Prof. Lee for acouple number of times. Prof. Lee also wasinvited to present his results in NTU, NCKU,and NSYSU.• Participants from institutions with lessresources: We have invited and interactedwith quite a few such speakers: Prof. Jyh-Shyang Wang and Prof. Ji-Lin Shen (Chung-Yuan Christian U.), Shih-Jye Sun(Kauhsiung U.)Training for young generation physicists:(i) Ph.D. student, Lu Yao Wang, was invited toattend a workshop on spintronics, by theorganizer Prof. Brataas, in the Center forAdvanced Studies in Oslo for two months:Sept. and Oct. of 2006. C. S. Chu alsovisited the same place in Sept. 2006. Theworkshop lasted one year, with invitedscientists working on spintronics discussingtheir findings and sharing their insights inan informal way.(ii). Invited visits to internationally prestigiousinstitutions by our young scholars:APCTP, Pohang, Korea: H.H. Lin (Aug.2007) and C.H. Chung (Feb. 2007)KITP, Santa Barbara, USA: C.H. Chung(Aug. 2007)KITPC, Beijing, China: C.H. Chung andH.H. Lin (Jul. 2007)(iii). A one-day PhD students workshoporganized by the NCTS post-doc, Kao-Chin Lin, and Ph.D. students in the Focusgroup is to be held on Sept. 8, 2007. Thisis intended to be a meeting for theseyoung physicists to discuss, to share, andto collaborate.(iv). C.H. Chung and H.H. Lin's studentsattended the joint summer school jointlyby APCTP and Max-Planck Dresden onstrongly correlated systems in nanostuctures,Jul. 2007, Pohang, Korea.III. Visitors and InternationalCollaborations• G. Mal'shukov (NCTS visiting professorfrom Moscow), R. Winkler (Argonne Lab.),Prof. E.I. Rashba (Harvard): visitors andcollaborators of Chon Saar Chu and Cheng-Hung Chang.• W. Hofstetter (Frankfurt U.): visitor andcollaborator of Chung-Hou Chung• Wei-Tong Sheng (Fudan U., China): visitorand collaborator of Shun-Ren Cheng.• Toshiya Hikihara (Hokkaido U.), Dung-HaiLee (UC Bekerley), Gil Rafael (Cal Tech):international collaborators of Hsiu-Hau Lin.• Peter Woelfle (Karlsruhe, Germany),Matthias Vojta (Koeln, Germany), GergelyZarand (Budapest, Hungary), Pascal Simon(Grenoble, France), Kevin Ingresent (U.Florida), Subir Sachdev and Lars Fritz(Harvard), Karyn Le Hur (Yale), LeonBalents (KITP, UCSB), Guang-Ming Zhang(Tsing Hua, Beijing), Lu Yu (AcademiaSinica, Beijing), Yong Baek Kim (Toronto):international collaborators with Chung-HouChung129 ‹‹- Highlights of Programs

• E. Abrahams (Rutgers, USA), V.Dobrosavljevic (Tallahassee, USA), V.Kagalovsky (Beer-Sheva, Israel), S.V.Kravchenko (Boston, USA), V. Mitin(Buffalo, USA), Y. Ochiai (Chiba, Japan), D.Popovic (Tallahassee, USA) , A. Punnoose(New York, USA) , G. Senatore (Trieste,Italy), A. A. Shashkin (Chernogolovka,Russia): visitors for disorder and localizationworkshop.• Y.C. Lee (SUNY, Buffalo): long-term visitor,March-July, 2007.IV. Highlights of Research Results• Chon Saar Chu(i). We consider the spin accumulation in theneighborhood of a normal scatterer in aRashba-type 2DEG. We find there is spinaccumulation–spin dipole–in the presenceof a driving electric field, even though it iswell known that the electric field could notgenerate a transverse spin current(ii). We consider the spin accumulation effectdue to spin-orbit interaction (SOI) arisingfrom in-plane potential gradient. In a2DEG in which a driving electric fielddoes not give rise to a spin current, wefind, again, spin dipole in theneighborhood of a ring-shaped potentialpattern. More importantly, the dipolestrength is greatly amplified near aquantum resonance, and the resonantcharacteristics allow for an electrical meanof switching the sign of the spin direction:by a gate-control of the chemical potentialof the system.(iii). We found the polarization of electrons ina symmetric quantum well by aperpendicular electric current due to therevival of a Dresselhaus SOI term.Averaging with the confined state in thequantum well, this term is zero. But in thepresence of a perpendicular electriccurrent this Dresselhaus SOI becomesfinite.• Chung-Hou Chung(i). We proposed (for the first time) theexperimental realization of the quantumcritical non-Fermi liquid state, originallydiscovered in the 2-impurity Kondo model,in the coupled double quantum dotsystems. We clarify a common misleadingbelief that particle-hole asymmetry wouldsmear out the transition. It has beenpresented in invited conference talks inDresden, Germany by Zarand (2007) , inAPCTP, Korea and in KITPC, Beijing byC.H. Chung (2007).(ii). We found a new type of quantum phasetransition between localized anddelocalized phases in a dissipativequantum dot. Our analyticalRenormalization Group (RG) andNumerical RG calculations reach anexcellent agreement. This work waspresented by K. Ingresent in a conferencein Dresden, Aug. 07'.(iii). We found a new scaling behavior for adissipative quantum dot coupled toLuttinger-liquid leads at non-equilibriumquantum criticality.C.H. C acknowledges the general supportfrom the NCTS. Its activities play animportant role in carrying out the abovementionedwork. Part of his work wasdone in collaboration with the NCTSvisitor W. Hofstetter.• Hsiu-Hau Lin(i) Develop self-consistent Green's functionmethod to describe the diluted magneticsemiconductor.(ii) Discover the role of Fermi surfacetopology in carrier-mediatedferromagnetism for spintronics devices.(iii) Demonstrate dynamical symmetryenlargement in carbon nanotubes by thecombination of renormalization group andbosonization techniques.• Cheng-Hung ChangThe semiclassical path integral (SPI)Highlights of Programs -›› 130

method has been successfully applied toexplain spin dynamics in several mesoscopicsystems under Rashba spin orbit interaction,including spin current transports and spinrelaxations. Recently we extend theapplication of this technique to spin relaxationproblems in quasi-1D channel under Rashbaspin-orbit interaction. By applying SPImethod, our recent preprint confirms severalprevious discoveries and predictions. Itclarifies the underlying mechanism responsiblefor those phenomena, extends the validity ofsome prediction, and derives and numericallyconfirms the Bessel-function spin relaxation insuch quasi-1D channel.• Shun-Jen ChengWe study spin characteristics of excitonicabsorption in self-assembled quantum dots.We carry out a theoretical investigation ofspin-characteristic excitonic absorption inbias-controlled charged quantum dots. SpinPauli blockade, Coulomb (exchange andcorrelation) interactions, and symmetry of dotshape are identified as the three mainunderlying mechanisms, sensitively dependingon N e , in the spin characteristic spectra. We forthe first time reveal that polarized absorptionin triply charged dots exhibits anomalous spindependentfeatures, resulting from the intrinsiccorrelations in charged exciton X -3 .• Yu-Chang ChenWe discuss how the shot noise in quantumchannels is affected by the quantum nature ofthe transverse momenta K in ballistic regime.We demonstrate, from first principlecalculations that the Fano factor may increaselinearly with the number of well-separatedparallel wires by the interference effectsthrough the reservoirs. This is in sharp contrastto the case of mesoscopic system, where theFano factor is independent of the number ofwell-separated parallel wires because of therestoration of quantized parallel channels.These research activities are collaborated withProf. Di Ventra at UCSD and Prof. Z. Yang atFudan University, who visited Taiwan sponsorby NCTS in 2006 and 2007.V. Selected Publications(for more details, please see http://phys.cts.nthu.edu.tw)[1] A.G. Mal'shukov, and C.S. Chu, Phys.Rev. Lett. 97, 76601 (2006).[2] A.G. Mal'shukov, L.Y. Wang, and C.S.Chu, Phys. Rev. B 75, 85315 (2007).[3] K.Y. Chen, C.S. Chu, and A.G.Mal'shukov, Phys. Rev. B (2007)(accepted).[4]. G. Zarand, Chung-Hou Chung, P. Simonand M. Vojta, Phys. Rev. Lett. 97 166802(2006).[5]. Chung-Hou Chung and Walter HofstetterPhys. Rev. B 76 045329 (2007).[6] Chung-Hou Chung, Matthew Glossop,Lars Fritz, Marijana Kircan, KivenIngersent, and Matthias Vojta., condmat/0706.2085(2007) (Physical Review Baccepted).[7] J. E. Bunder and Hsiu-Hau Lin*, Phys.Rev. B 75, 075418 (2007).[8] Wen-Min Huang, Cheng-Hung Chang andHsiu-Hau Lin*, Phys. Rev. B 73,241307(R) (2006).[9] J. E. Bunder, Shih-Jye Sun and Hsiu-HauLin*, Appl. Phys. Lett. 89, 072101 (2006).[10]. Wen-Hsuan Kuan, Chi-Shung Tang,Cheng-Hung Chang, Phys. Rev. B 75,155326 (2007).[11]. Wen-Min Huang, Cheng-Hung Chang,Hsiu-Hau Lin, Phys. Rev. B 73,241307(R) (2006).[12] S.-J. Cheng, Phys. Rev. B 76, 075329(2007).[13]. J.Yao, Y-.C. Chen, M.Di Ventra and Z.Yang, Phys. Rev. B 73, 233407 (2006).[14]. Z. Huang, B. Xu, Y.-C. Chen, M. DiVentra and N.J. Tao, Nano Lett. 6, 1240(2006).131 ‹‹- Highlights of Programs

Focus Group of Novel Quantum Phenomena inCondensed MatterCoordinator: Chung-Yu Mou (National Tsing Hua University; email: mou@phys.nthu.edu.tw)Wen-Chin Wu (National Taiwan Normal University; email: wu@phy.ntnu.edu.tw)Committee members: Yung-Chung Chen (Tung Hai University), Chung-Hou Chung (National Chiao Tung University),Di-Jing Huang (National Synchrotron Radiation Research Center),Chang-Ming Ho (Tamkang University),Ying-Jer Kao (National Taiwan University),Hsiu-Hau Lin (National Center for Theoretical Sciences and National Tsing Hua University),Jiunn-Yuan Lin (National Chiao Tung University), Shin-Tza Wu (National Chung Cheng University)I. Brief Descriptionhe "Novel Quantum Phenomena inCondensed Matter (NQPCM)" focusgroup is the newly combined one of previous"Spin-Related Physics in Condensed Matter(SRPCM)" (led by Chong-Der Hu) and"Strongly Correlated Electron Systems(SCES)" (led by Chung-Yu Mou) focusgroups. Its goal is to provide a platform for thecondensed matter theorists in greater Taiwanto interact strongly with each other, andultimately work together to focus on somefrontier areas. To achieve this goal, a programcommittee is formed and devoted to promotemutual interactions in all formats that lead tofruitful collaborations.In addition to committee members,currently there are twenty active members(professors) and twenty young members(postdocs & senior graduate students) or so.Focused topics selected and studied by groupmembers are: (1) Superconductors & Oxides,(2) Spintronics and spin Hall effect, (3)Multiferroics, (4) Low-dimensional system(graphene, quantum dot, nanotube, etc.), (5)Strongly correlated system of cold atoms, (6)Numerical methods in strongly correlatedelectronic systems, and (7) Quantumcomputing.II. ActivitiesDuring past one year period, the activitiesorganized or sponsored by our group are:(1) The Fifth Joint Workshop on Physics ofMetal Oxides: Experiment and Theory,2006/12/01-03, Yi-Lan.(2) The 6th Asia-Pacific Workshop onFrontiers of Condensed-Matter Science andSymposium on 20-years Anniversary ofDiscovery of YBCO: 2007/04/13-16,Taipei.(3) 2007 Summer Workshop on NovelQuantum Phenomena in CondensedMatter: 2007/07/13 -15, NDHU.(4) Miniworkshop on Numerical Method inStrongly Correlated Electronic Systems:2007/12/14, NTHU.(5) The topic program on Superconductivityand Magnetism at Nanoscale: Effects ofquantum fluctuations and disorder:2007/12/01 - 2008/01/31, NCTS.Activity details can be accessed via:http://phys.cts.nthu.edu.tw/research/focus_group.php?Sn=36.Activities (2) & (5) are aiming at inducingpossible cooperation among participants andforeign visitors on frontier areas in condensedmatter physics. They are also useful to makeour scientific results more visible. Activities(1), (3), & (4) are aimed at providing aplatform for domestic condensed matterexperimentalists and theorists to work togetherHighlights of Programs -›› 132

on selected hot topics. They are also importantin introducing new fields and/or newtheoretical technique to young researchers. Inaddition to the above activities, weaklycondensed matter seminars are organized inNTU & NTHU/NCTU (occasionally also inother universities). There are also visitingprograms hosted in NCTS during the summerand winter time. To train young generation,travel funding is awarded on the priority ofyoung researchers.III. Visitors and InternationalCollaborations(1) International Visitors(Dec. 06 ~ Dec. 07)Konstantin Bliokh (Ukraine), Koung-AnChao (Lund), Steven Girvin (Yale), EberhardGross (Berlin Free), Toshiya Hikihara(Hokkaido), Fabian Heidrich-Meisner(ORNL), Hae-Young Kee (Toronto), Yong-Baek Kim (Toronto), Dung-Hai Lee (UCBerkeley), Yung-Chang Lee (SUNY Buffalo),Sadamichi Maekawa (Tohoku), Choo Hiap Oh(Singapore), Gil Rafael (Caltech), EmmanuelIosifovich Rashba (Harvard), Anders Sandvik(Boston), Krishnadu Sengupta (India), IvanSergienko (ORNL), Shun-Qing Shen (HongKong), Chin-Sen Ting (Houston), DavidThouless (Washington, Seattle), Xincheng Xie(Oklahoma State), Nei-Chang Yeh (Caltech).(2) International Collaborations• Ting-Kuo Lee (AS), Chang-Ming Ho, Chi-Tin Shih (THU) + Tao Xiang (Chin AcadSci, Beijing), Fu-Chun Zhang (Chinese U,HK) on the problems of high-Tc.• Ming-Che Chang (NTNU) + Qian Niu(Austin) on the problems of spin Hall effect.• Chung-Hou Chung+ Walter Hofstetter(Johann Wolfgang Goethe-U), GergelyZarand (Karlsruhe), Matthias Vojta(Karlsruhe), K. Ingerson (Florida) and etc.on the problems of quantum dots.• Yong-Chung Chen + Fabian Heidrich-Meisner (ORNL) on applying DMRGmethod in quantum spin systems.• Ying-Jer Kao+ Anders Sandvik on theeffects of doped impurities in spin models;development of numerical methods instrongly correlated systems.• Ying-Jer Kao + Roger Melko (Waterloo),Stefan Wessel (Stuttgart) on supersolidphases in lattice boson models.• Ying-Jer Kao + Yong-Baek Kim, Hae-YoungKee, Michel Gingras (Waterloo) on aspectsof frustrated systems.• Hsi-Sheng Goan (NTU) + Gerard J. Milburn(Queensland), Choo Hiap Oh, Xiao-ZhongYuan (Shanghai Jiao Tong U), Xin-Qi Li(Beijing) on topics of quantum computing.IV. Highlights of Research Results(1) Superconductors and oxides:Ting-Kuo Lee, Chang-Ming Ho, Chi-TinShih and their collaborators have studied thespectral weights for adding and removing anelectron of the Gutzwiller projected d-wavesuperconducting state of the t-J-type models.They show that the product of weights is thesame as in the weakly coupled case. Arigorous relation of spectral weights withdoping in the electron doped system wasderived with consistent results with theexperiments [1]. They also studied moresystematically the low-energy physicalproperties of the plain vanilla d-wave RVBstate. Overall qualitative agreement with theexperiments is obtained [2].Wen-Chin Wu and Cheng-Shi Liu havestudied extensively the coexistence of an AForder and the d-wave superconducting orderparameter in electron-doped cupratesuperconductors. Through the investigation ofRaman scattering, neutron scattering, and thedoping-dependent [110] Andreev bound states,positive and consistent results are obtainedwhen the experiments are compared [3].(2) Spintronics and spin Hall effect:Hsiu-Hau Lin and his collaborators havedeveloped a self-consistent Green's functionmethod to describe the diluted magneticsemiconductors [4]. The role of Fermi surface133 ‹‹- Highlights of Programs

topology is discovered in carrier-mediatedferromagnetism for spintronics devices [5].The dynamical symmetry enlargement hasbeen demonstrated in carbon nanotubes by thecombination of renormalization group andbosonization techniques [6].Using a semiclassical approach, Ming-CheChang and Qian Niu have demonstrated that itis necessary and sufficient to include the Berrycurvature and orbital moment in order toaccount for all physical effects to first order inexternal fields. They show that these gaugeinvariant quantities are also sufficient for acorrect quantum theory. They apply the ideasto semiconductor bands, and show how theeffective theories in a hierarchy shouldrenormalize [submitted].Ching-Ray Chang (NTU) and hiscollaborators have investigated electron spinprecession in nonuniform Rashba-Dresselhaustwo-dimensional electron systems alongarbitrary continuous paths [7]. A persistentspin helix in spin-orbit coupled twodimensionalelectron systems, predictedrecently to exist in two particular cases, is alsoinvestigated [8].(3) MultiferroicsAs a joint effort between theorists andexperimentalists, Di-Jing Huang, Chung-YuMou and their collaborators recently proposedthe idea of an internal electric field to explainthe behavior of multiferroics in TbMn 2 O 5 . Theelectric field is composed by quadraticcombination of Fourier transformation of themagnetic order parameter. The soft x-ray datashows excellent agreement with the theory.The paper was accepted by PRL [9].Chong-Der Hu (NTU) studied the magneticoxides, in which ferroelectricity coincides withthe onset of a second incommensuratemagnetic order. The wave function of E gelectrons is solved. The coupling between themagnetic and electric orders is provided by thespin-orbit interaction. It was found that the netelectric dipole moment of the system camefrom the bond between the transition metaland oxygen atoms[10].Guan-Yu Guo (NTU) and his collaboratorshave investigated an electrically controllablespin filter based on multiferroic tunnelingjunction. This spin filter combines theexchange splitting of ferromagnets andasymmetry in energy potential due to thescreening of ferroelectric polarization chargesat electrodes. Calculations show an enhancedspin filtering efficiency and a positive-tonegativetunneling magnetoresistance [11].(4) Low-dimensional systemChung-Hou Chung and his collaboratorshave focused on quantum phase transitions andcharge transports in semiconductor quantumdots. They successfully showed the Kondo-tospinsinglet phase transition/crossover basedon a simple setup and have applied thenumerical renormalization group (NRG)method to extract the transmission coefficientthrough the double dots [12]. In addition, theyhave proposed the realization of the quantumcritical non-Fermi liquid state in the doubledot systems [13]. For this excellent work,Chung gave an invited talk at the workshop inAsia-Pacific Center for Theoretical Physics(APCTP) on quantum criticality (Pohang,Korea, 2007/02). Paper [13] was selected asthe Highlights of the Poster Session in theinternational conference in strongly correlatedelectron systems (Houston, 2007/05).Chung and his collaborators have alsomanaged to obtain NRG results for thepseudogap Bose-Fermi Anderson model forspinless electrons. The NRG results are ingood agreement with the analytical RGpredictions [14].(5) Strongly correlated system of cold atomsChien-Hua Pao (CCU), Shin-Tza Wu, andSungkit Yip (AS) have worked on BEC-BCScrossovers in cold atoms. One of their earlierpapers [15] has recently been selected as aNew Hot Paper by the Thomson Corporation'sEssential Science Indicators. (Seehttp://www.esi-topics.com/nhp/2007/july-07-Pao-Wu-Yip.html.) More recently they workon the general case of pairing betweenfermions of unequal masses. For the unitarilylimit, a regime which has most experimentalinterests currently, they have just published apaper based on a mean-field study [16]. AHighlights of Programs -›› 134

paper that extends to general couplingstrengths is just submitted.(6) Numerical methods in strongly correlatedelectronic systemsYing-Jer Kao and his collaborators haveidentified a realization of the random-fieldIsing model. They show in L i HO X Y 1–X F 4 thatthe field-induced magnetization along xdirection, combined with the local randomdilution-induced destruction of crystallinemirror symmetries generates random fieldsalong the Ising z direction. This identifiesL i HO X Y 1–X F 4 in B x as a new random field Isingsystem [17]. Kao and his collaborators havealso studied the effects of Fermi-surfacefluctuations on the single-particle lifetime nearthe diagonal electronic nematic phase on a 2Dsquare lattice. They showed that there exists aquantum critical point between the diagonalnematic and isotropic phases [18].In addition, Kao and his collaborators haverecently studied in details the ground statephases of the hardcore boson-Hubbard modelon the square lattice [submitted].Independently Yong-Chung Chen, Chung-HouChung, and their collaborators investigated thetriangular and Kagome lattices [submitted].The numerical methods employed by bothteams including Gutzwiller mean field,variational Monte Carlo, and quantum MonteCarlo.(7) Quantum computingHsi-Sheng Goan and his collaborators haveinvestigated the non-Markovian decoherenceand entanglement dynamics of one or twocentral spins under respectively the quantumHeisenberg XY spin [19] andantiferromagnetic [20] environments. The non-Markovian entanglement dynamics of twointeracting nano-mechanical oscillators inthermal environments is also studied [21]. Ascheme for implementing unconventionalgeometric quantum computation by using theinteraction of two atoms with a two-modecavity field has also been proposed [22].Owing to these excellent works, Goan wasinvited to speak at the International Workshopon Quantum Dynamics and BiomolecularFunction (Yeppoon, Australia).V. Selected PublicationWe apologize that group members associated withpublications [1,2,7,8,12-14] forgot to acknowledge thesupport of NCTS in the papers. These are definitelyresearch results under the support of NCTS.[1] C.-P. Chou, T.K. Lee, and C.M. Ho, Phys.Rev. B?74, 092503 (2006).[2] K.Y. Yang, C.T. Shih, C.-P. Chou, S.M.Huang, T.K. Lee, T. Xiang, F.C. Zhang,Phys. Rev. B 73, 224513 (2006).[3] C.S. Liu and W.C. Wu, Phys. Rev. B 76,014513 (2007); submitted (2007).[4] J.E. Bunder, S.-J. Sun, and H.-H. Lin,Appl. Phys. Lett. 89, 072101 (2006).[5] W.-M. Huang, C.-H Chang, and H.-H. Lin,Phys. Rev. B 73, 241307(R) (2006).[6] J.E. Bunder and H.-H. Lin, Phys. Rev. B75, 075418 (2007).[7] M.H. Liu, C.-R. Chang and etc., Phys. Rev.B 74, 235322 (2006).[8] M.-H. Liu and C.-R. Chang, Phys. Rev. B74, 195374, (2006).[9] J. Okamoto, D.J. Huang, C.-Y. Mou, andetc., Phys. Rev. Lett., 98, 157202 (2007).[10] C.D. Hu, Phys. Rev. B 75, 172106 (2007).[11] S. Ju, T.Y. Cai, G.Y. Guo, Z.Y. Li, Phys.Rev. B 75, 064419 (2007).[12] C.-H. Chung and W.Hofstetter, Phys. Rev.B, in press (2007).[13] G.Zarand, C.-H. Chung, P. Simon, and M.Vojta, Phys. Rev. Lett. 97, 166802 (2006).[14] C.-H. Chung, M. Glossop, L. Fritz, M.Kircan, K. Ingersent, and M. Vojta, Phys.Rev. B, in press (2007).[15] C.-H. Pao, S.-T. Wu, and S.K. Yip, Phys.Rev. B 73, 132506 (2006).[16] S.-T. Wu, C.-H. Pao, and S.K. Yip, Phys.Rev. B 74, 224504 (2006).[17] S. M. A. Tabei, M. J. P. Gingras, Y.-J.Kao, P. Stasiak, and J.-Y. Fortin, Phys.Rev. Lett. 97, 237203 (2006).[18] Y.-J. Kao, H.-Y. Kee, Phys. Rev. B 76,045106 (2007).[19] X.Z. Yuan, H.-S. Goan, and K.D. Zhu,Phys. Rev. B 75, 045331 (2007).[20] X. Z. Yuan, H.-S. Goan and K. D. Zhu,New Journal of Physics 9, 219 (2007).[21] K.-L. Liu and H.-S. Goan, Phys. Rev. A76, 022312 (2007).[22] C. Wu, H.-S. Goan, C.H. Oh and etc.,Phys. Rev. A76, 024302 (2007).[23] Z. T. Kao, J. Y. Lin, and C. -Y. Mou,Phys. Rev. B 75, 012503 (2007).135 ‹‹- Highlights of Programs

Highlights of ProgramsParticles and FieldsFocus Group on Collider, Astroparticle and BSMCoordinator: Kingman Cheung (National Tsing Hua University and National Center for Theoretical Sciences;email: cheung@phys.nthu.edu.tw)Committee members: Wei-Shu Hou (National Taiwan University), Cheng-Wei Chiang (National Central University),Chung-Wen Kao (Chung Yuan Christian University), Chuan-Hung Chen (National Cheng Kung University),Tzu-Chiang Yuan (National Center for Theoretical Sciences)I. Introductione focus on collider phenomenologyand astroparticle physics, in relationto new physics beyond the standard model(SM).Most of us believe that the new physicsshould come in in the TeV scale. Many newmodels predict new particles or new dynamicsat TeV scale so as to halt the gauge hierarchy.There is a hope that the upcoming LHC is theplace for the next big discovery. Together withother planned cosmology experiments, testingnew ideas will be the major activities in thenext ten years. Our activities concentrate onthe particle physics phenomenology, whichlinks up the theory and experiments. We haveaccomplished a number of interestingpublished works, which are the consequeneceof our group activities.This year we have important results onHiggs boson searches and on "unparticle",which will be described later.II. Major Activities held in 2007(i) The Winter Program in January 2007 --quite a number of visitors during the Winterbreak, and we organized a number ofseminars. Most of them were about thedark matter. We have established acollaboration with Shigeki Matsumoto,Nobuchika Okada of KEK, and EibunSeneha of NCU to work on the light-stopbaryogenesis scenario. It is still inprogress.(ii) The 7th Particle Physics PhenomenologyWorkshop, June 2007 -- jointly organizedby the focus groups on particle physics inHsinchu and Taipei. This is a biannualmeeting of particle phenomenology inTaiwan.(iii) A Joint Summer Institute -- during Juneand July 2007 was organized by the focusgroups on particle physics in Taipei andHsinchu. We made use a group of visitorsof PPP7 and invited them to stay longer sothat we could have more interactions. Wehave established a collaboration with Jae-Sik Lee of SNU to work on the Higgsboson decay in CP violating MSSMscenario. It is under investigation.(iv) Workshop on Unparticle Physics in June2007 jointly organized by the focus groupson particle physics in Hsinchu, Taipei, andTainan.This is an urgent responseworkshop to a new emergent topic --Highlights of Programs -›› 136

Unparticle. Taiwan has three groupsworking on this topic since the first paperby Georgi. We have studied the mostimportant features of the unparticle andrelated them to experiments. We will givemore details below. The aim of theworkshop was to further strengthen theactivities in this area and promote furthercollaborations. Students are benefittedfrom this workshop.III. Visitors and InternationalCollaborationsTom Weiler (Vanderbilt U.), NobuchikaOkada (KEK), Shigeki Matsumoto (KEK),Jeonghyeon Song (Konkuk U.), HiroakiSugiyama (KEK), Masaki Asano (KEK),Yasuhiro Okada (KEK), Wai-Yee Keung(UIC), Chung Kao (Oklahoma U.), Ian Low(UC-Irvine), Lock-Seng Goh (Arizona U.), JaeSik Lee (SNU), C.S. Kim (Yonsei U.), K. Tobe(Tohoku U.).We have invited Wai-Yee Keung to join themulti-year visitor program of the NCTS. Thisyear with his visit, Kingman Cheung, Wai-YeeKeung, and Tzu-Chiang Yuan have written animportant paper on "unparticle physics",accepted by Phys. Rev. Lett.We have also established a collaboration withJeonghyeon Song of Konkuk U. KingmanCheung, Qi-Shu Yan (a postdoc in NTHU),and Song have written a paper on "Role of h→ηηin intermediate-mass Higgs bosonsearches at the LHC", which is now publishedin Phys. Rev. Lett. Details will be givenbelow.We have also established a collaborationwith Nobuchika Okada and ShigekiMatsumoto of KEK, together with EibunSeneha of NCU.IV. Highlights of Research Results(i) A twist in the search for the Higgs bosonThe title of the paper is "Role of h → ηη inthe search of intermediate-mass Higgs bosonat the Large Hadron Collider", authored byKingman Cheung, Jeonghyeon Song, and Qi-Shu Yan, published in Phys. Rev. Lett.The emergence of the Higgs boson decaymode into two pseudoscalar bosons, which canrelieve the so-called little hierarchy problemand reduce the LEP2 Higgs boson mass bound,may affect the golden search modes (h →γγ,bb – ) of the Higgs boson significantly. The LHCmay not be able to find the Higgs boson if thetwo-pseudoscalar decay mode dominates. Ourwork explicitly shows that the associatedproduction of the Higgs boson with a W or Zboson can recover the loss of sensitivity in thegolden modes. With the Higgs bosondecaying into two pseudoscalar bosons, whichfurther decay into 4 b jets, together with atleast a charged lepton from the W or Z bosondecay, a significant Higgs boson signal isobservable at the LHC. The ultimate goal ofthe LHC is hunt for the Higgs boson, which isresponsible for electroweak symmetrybreaking and mass generation.We show in Fig. 1 the invariant massspectrum of the 4 b-tagged jets. The peakclearly shows the presence of the Higgs boson,which stand out of the continuumbackgrounds. With the crucial cut of M 4b onecan also reconstruct the mass bump of the η's.(ii) Novel signals in unparticle physicsThe paper was authored by KingmanCheung, Wai-Yee Keung, and Tzu-ChiangYuan, and has been accepted by Phys. Rev.Lett.Recently perceived by Georgi a scaleinvariant sector with a non-trivial infraredfixed point at a higher energy scale may137 ‹‹- Highlights of Programs

actually describe the real world at high energy.The unparticle with a scale dimension d U canbe interpreted as a collection of d U invisiblemassless particles, which can be unveiled bymeasurements of various energy distributionsin the processes Z → ƒƒ – U and e - e + →γU ate - e + colliders, as well as mono-jet productionat hadron colliders.The new result of our Letter is thepropagator effect of the unparticle. The novelfeatures, induced by scale invariance, include aspectacular phase factor exp(-i d U π) associatedwith the propagator in s-channel. Such afactor can give rise to non-trivial behavior in anumber of processes. We studied the effects inthe Drell-Yan process and in the one-loopmuon anomaly. In Fig.2, we show thefractional difference from the standard modelprediction around the Z pole. Interestinginterference pattern can be seen clearly.V. Publications[1] K. Cheung, W.Y. Keung and T.C. Yuan,"Collider Phenomenology of UnparticlePhysics," Phys. Rev. D76, 055003 (2007).[2] K. Cheung, W.Y. Keung and T.C. Yuan,"Novel signals in unparticle physics,"Phys. Rev. Lett. 99, 051803 (2007).[3] K. Cheung, J. Song and Q.S. Yan, "Role ofh →ηηin the search of intermediate-massHiggs boson at the LHC", Phys. Rev. Lett.99, 031801 (2007).[4] K. Cheung, S.K. Kang, C.S. Kim and J.Lee, "Correlation between lepton flavorviolation and B (d,s) – B – (d,s) mixing in SUSYGUT," Phys. Lett. B652, 319 (2007).[5] K. Cheung and T.C. Yuan, "Hiddenfermion as milli-charged dark matter inStueckelberg Z' model,'' JHEP 0703, 120(2007).[6] K. Cheung and J. Song, "Lightpseudoscalar η and H →ηηdecay in thesimplest little Higgs model," Phys. Rev.D76, 035007 (2007).[7] K. Cheung, C.S. Kim, K.Y. Lee and J.Song, "Associated production of a singleheavy T-quark in the littlest and simplestlittle Higgs models", Phys. Rev. D74,115013 (2006).[8] A. Arhrib, K.-Cheung, T.-J.-Hou and K.-W.-Song, "Associated production of a lightpseudoscalar Higgs boson with a charginopair in the NMSSM," JHEP 0703, 073(2007).[9] C.S. Chen, K. Cheung and T.C. Yuan,"Novel collider signature for little Higgsdark matter models," Phys. Lett. B644, 158(2007).[10] C.W. Chiang and E. Senaha, "Updateanalysis of two-body charmed B mesondecays", Phys. Rev. D75, 074021 (2007).[11] W.S. Hou, H.-N. Li, S. Mishima, and M.Nagashima, "Fourth generation CPviolation effect on B → Kπ, φK and ρK inNLO PQCD", Phys. Rev. Lett. 98, 131801(2007).Highlights of Programs -›› 138

Focus Group on Gravitation, Cosmology andQuantum GravityCoordinator: Hoi-Lai Yu (Academia Sinica; email: hlyu@phys.sinica.edu.tw)Committee members: Chiang-Mei Chen (National Central University), Hing-Tong Cho (Tamkang University),Da-Shin Lee (National Dong Hwa University), Wo-Lung, Lee (National Taiwan Normal University),James Michael Nester (National Central University), Kin-Wang Ng (Academia Sinica),Chopin Soo (National Cheng Kung University), Hwei-Jang Yo (National Cheng Kung University)l. Brief Descriptionhe subject materials that we haveidentified so far are not only thehottest current research topics, moreimportant, these are the areas that ourcommunity have enough technical know how,expertise, and insights to make majorcontributions.In Cosmology:To investigate the detailed mechanisms ofinflation from non-equilibrium point ofview(in particular, stochastic inflation) andcompare with CMB data and large scalestructures of the universe; the origin of darkmatter within or beyond the Standard Model;the physics, properties, and origin of darkenergy.In General Relativity:Gravitational energy, gravitational radiationreactions and quasi-normal modes of blackholes which affect lots of topics in cosmologywill be our main activities.In Quantum Gravity:Canonical quantization of gravity usingAshtekar variables, stochastic gravity usingclosed-time-path techniques, and quantum toclassical transitions will be studied.Major members of our focus group are:Chiang-Mei Chen (NCU) on gravitation andstring theoriesHing-Tong Cho (TKU) on gravitation andblack holesDa-Shin Lee (NDHU) on non-equilibriumphysics and cosmologyWo-Lung Lee (NTNU) on large scalestructures of UniverseJames Michael Nester (NCU) on gravitationand Quasi-local massesKin-Wang Ng (Academia Sinica) oncosmology and data analysisChopin Soo (NCKU) on quantizing gravityand cosmologyHwei-Jang Yo (NCKU) on numerical generalrelativityHoi-Lai Yu (Academia Sinica) on quantizinggravity and cosmologyFrequent visitors are:Bei-Lok Hu (University of Maryland);Roh-Suan Tung (Shanghai NormalUniversity);Yun-Kau Lau (Applied Mathematics Institute,Academia Sinica, Bejing);Larry H. Ford (Tufts University);Misao Sasaki (Kyoto University);Ray Rivers (University of London).The purposes of this focus group are:(1) To generate long-term collective force inCosmology and Gravity be searchedactivities among the local communities andAsia Pacific areas;(2) Using non-equilibrium field theories andgeneral relativity as keys to generateinterdisciplinary and cutting-edge research139 ‹‹- Highlights of Programs

activities on cosmology, classical andquantum gravity and quantum informationscience;(3) To train and create chances for talentedgraduate students and postdocs to makemajor contributions by helping them toidentify hot and important interdisciplinaryproblems in the area of cosmology,gravitation and quantum gravity.ll. ActivitiesThe following major activities are carriedout last year on top of our regular/irregularjournal club meetings in Institute of Physics,Academia Sinica and Department of Physics,National Central University.(1) 2007 Tainan School and Workshop onCosmology and Gravitation at NCKU(13 th – 16 th January, 2007):This was the first school/workshop in thisfield in Taiwan so far. The main purpose ofthis meeting is to introduce to students andresearchers the latest developments instochastic quantum gravity, cosmology andsemi-classical quantum gravity.We have about 70 graduate students,postdocs and local faculities and faculties fromAsia Pacific area in the meeting. Majorlectures were delivered by researcher fromoverseas:L. Ford (Tufts U.), Bei-Lok Hu(Maryland U.), Misao Sasaki (Kyoto U.),Albert Roura(Los Alamos), E. Verdaguer(Universitat de Barcelona), Y. K. Lau (Inst. ofApplied Math., Academica Sinica, Beijing), R.S. Tung (Shanghai Normal U.)Research topics in applying stochasticgravity to cosmology and black holes werecarried out by D.S. Lee, K.W. Ng, W.L. Leeand H.T. Cho among group membersimmediately after the workshop and paperswere also published (see publication list in thebelow) in these related areas.(2) 2007 Taipei School/Workshop on LargeScale Structures of the Universe(28 th May– 2 nd June, 2007, NTNU):Though the discovery of dark energy led usventuring into an uncharted territory, largepiles of precise observational data and efficientnumerical techniques have helped the study onthe Universe continue to thrive in the 21stcentury.The purpose of this School/Workshopwas to introduce students and faculties inTaiwan the progress and the state of the art inthis fascinating frontier of physics andastronomy. The lectures were delivered by:Li-Zhi Fang( Dept. of Physics, Universityof Arizona), Prof. Houjun Mo( Dept. ofAstronomy, Univ. of Massachusetts), Prof.Yipeng Jing(Shanghai AstronomicalObservatory), Prof. Long-Long Feng(PurpleMountain Observatory)(3) Collaborate with the QuantumInformation Sciences focus group inrunning the Summer School on NonequilibriumDynamics and QuantumCoherence (4 th – 6 th July, 2007, NCKU)This Summer School on Non-equilibriumDynamics and Quantum CoherencePhenomena was aimed to provide the basicideas and concepts of the method of nonequilibriumtheory including the Feynman-Vernon and coherent state path integralformulation, and Schwinger- Keldysh's nonequilibriumGreen's function method. Thelecturers from our focus group members andvisitors are: B. L. Hu and D. S. Lee.We want to emphasize that our postdocs,C.S Chou's and S.Y. Lin's works on topics onQuantum Entanglement and Moving Atoms inQuantum Fields provide excellent exampleson how interdisciplinary works between nonequilibriumfield theories, general relativityand quantum information science can becombined coherently to achieve majorbreakthrough towards the understanding ofthese hot topics which have found importantapplications in quantum information scienceand the gravitational wave detecting LIGOphysics.(4) Visiting prestigious academic institutes(1) With the help of Prof. L. Ford and B.L.Hu our postdocs (S.Y. Lin, C.S. Chouand C.H. Wu)were arranged to visit andconduct research at PrincetonHighlights of Programs -›› 140

University, Univsersity of Maryland ,Tuft University and International Centerfor Gravitation Research at Universityof Pennsylvania.(2) With the help of Prof. Y.K. Lau, 10graduate students (from NCU, NDHUand NCKU) were arrange to attend thegravitation workshop at Institute ofApplied Mathematics, Academia Sincia,Bejing during the summer.III. Visitors and InternationalCollaborationsPlease refer to the above descriptions.IV. Highlights of Research Results(1) We have proved that black holes areelementary particles in superspace andquantum geometry with sphericalsymmetry is unitary and singularity free.This work will be published in PRD andH.L.Yu will be invited to deliver a talk atThe Eighth Asia-Pacific InternationalConference on Gravitation andAstrophysics held in Nara in 28 th , August,2007.(2) Obtained the most stringent limit on theparity violating coupling of Dark energy tolight by using observed cosmic microwavebackground power spectra. Phys. Rev. Lett.97, 161303 (2006).(3) Riemann normal coordinates: a completeaccounting; J. Phys. A: Math. Theor. 40,2751-54.(4) Prof. D.S. Lee is invited by Prof. R. Riversto visit London University and conductresearch on applying non-equilibriumtechniques to experimental studies ofanalog gravity using Bose-Einsteincondensation.(5) A reformulation of the Wheeler-DeWittequation which highlights the role ofgauge-invariant three-geometry elements ispresented in the general setting of theBarbero-Immirzi extension of Ashtekar'scontraints, and when a cosmologicalconstant is also present, Class. QuantumGrav. 24 (2007) 1547-1555.V. Publication[1] G. C. Liu, S. Lee and K. W. Ng, Phys. Rev.Lett. 97, 161303 (2006).[2] C. Soo, Class. Quantum Grav. 24, 1547-1555 (2007) .[3] J. Nester, J. Phys. A: Math. Theor. 40,2751-54 (2007).[4] H.T. Cho, A.S. Cornell, J. Doukas, and W.Naylor, Phys. Rev. D75, 104005 (2007).[5] H.-T. Cho and C.-L. Ho, J. Phys. A40,1325 (2007).[6] C.-M. Chen, D. V. Gal'tsov and D. G.Orlov, Phys. Rev. D75, 084030 (2007).[7] Shih-Yuin Lin and B. L. Hu, Phys. Rev. D73, 124018 (2006).[8] Shih-Yuin Lin and B. L. Hu, Phys. Rev. D,in press (2007).[9] C.H. Wu, K.W. Ng, W. Lee, D.S. Lee andY. Y. Charng, JCAP 0702006 (2007).[10] D.S. Lee, C. Y. Lin and R. J. Rivers,Phys. Rev. Lett. 98, 020603 (2007).[11] J.T. Hsiang, T.H. Wu, and D.S. Lee,arXiv:hep-th/0706.3075 (submitted toPhys. Rev. D ).[12] C.H. Chou, B. L. Hu and T. Yu,arXiv:quant-ph/0703088 (submitted toPhys. Rev. D ).[13] C.H. Chou, C. Soo and H.L. Yu, arXiv:grqc/0703072(to appear in Phys. Rev. D76,084004 (2007).Note: Some publications listed in this report may notacknowledge the support of NCTS. We apologize forsome members of the group who forgot to put it onthe papers. Those works are definitely researchresults under the support of NCTS.141 ‹‹- Highlights of Programs

Focus Group on Particle, Nuclear and CosmologyCoordinator: Ting-Wai Chiu (National Taiwan University; email: twchiu@phys.ntu.edu.tw)Committee members: Chia-Hung Chang (National Taiwan Normal University), Hai-Yang Cheng (Academia Sinica),Cheng-Wei Chiang (National Central University), Xiao-Gang He (National Taiwan University),Choon-Lin Ho (Tamkang University), Kin-Wang Ng (Academia Sinica),Kwei-Chou Yang (Chung-Yuan Christian University)I. Brief Descriptionhe main theme of PNC focus group isto tackle the important physics withinthe Standard Model (SM), as well as toidentify any signals which may suggest newphysics beyond the SM. To achieve this goal,we call for the collective efforts of theoristsand experimentalists. The topics under activeinvestigations are: (1) Phenomenologies ofStrong and Electroweak Interactions, (2)Flavor physics and CP violation, (3) Grandunification, (4) Supersymmetry, (5) Modelsbeyond the SM, (6) Hadron physics, (7)Effective Field Theory of QCD, (8) LatticeQCD, (9) Baryon asymmetry in the universe,(10) Accelerating universe and CMB effects.Even though our projects appear to cover awide range of topics, they are unified underthe main theme.II. ActivitiesOur weekly seminar and journal clubs are:(1) Particle physics journal club, (2)Theoretical physics seminar, (3) Cosmologyand astrophysics journal club, and (4) LatticeQCD journal club http://twcp3.phys.ntu.edu.tw/lqcdjc/. Among them, (4) is a newactivity which has started since March 2007.These weekly activities are crucial for thesuccesses of High Energy Physics in Taiwan.In particular, (1) has played a crucial role tobring HEP experimentalists and theoriststogether, which is crucial for the advancementsof the NTU Belle group as well as our B-physics phenomenologists. In fact, many newideas and insights were initiated at (1), throughintensive discussions among severalparticipants, and also between experimentalistsand theorists.Besides the regular weekly seminars andjournal clubs, we have The 20 th Spring Schoolin Particles and Fields http://www.phys.sinica.edu.tw/~ss2007/index.files/Page873.htmin April, and The 7 th Particle PhysicsPhenomenology Workshop http://phys.cts.ntu.edu.tw/ppp7 (PPP7) in June. The purposeof the Spring School is to introduce recent hottopics to graduate students at a pedagogicallevel. Also, it is one of the main activities inTaiwan HEP community. Most graduatestudents and faculty attend The Spring Schoolevery year. At PPP7, we had manydistinguished speakers from US and Japan,including the KEK Director Atsuto Suzuki,and former Belle spokesman Steve Olsen.There were many scientific discussions inPPP7, which may have impacts to thedevelopment of HEP. For example, duringPPP7, Steve Olsen and Ting-Wai Chiu hadmany discussions on the heavy charmoniumlikevector mesons, which indeed motivatedBelle Collaboration to search for chargedheavy meson. In August, Belle announced thediscovery of a new charged resonance Z(4430)[arXiv:0708.3496]. This would be the firstobservation of a genuine tetraquarkcharmonium state.III. Visitors and InternationalCollaborationsDuring 2006-2007, we have set up anHighlights of Programs -›› 142

international collaboration between JLQCDand TWQCD Collaborations. It is well knownthat JLQCD Collaboration constitutes an elitegroup of lattice field theorists, who have beenplaying a vital role in the lattice QCDcommunity. Since 2006, JLQCD has startedthe project of simulating dynamical overlapfermion using the newly installed IBMBlueGene supercomputer with peak speed ~50Teraflops. In the summer of 2005, ShojiHashimoto (the group leader of JLQCD) askedTing-Wai Chiu and TWQCD members tocollaborate with JLQCD on the dynamicaloverlap project. Since then, we have had manymutual visits between JLQCD and TWQCD,and now we have worked out severalimportant results (see Sections IV and V).Furthermore, we also encourage local people(faculty and graduate students) to work onlattice QCD, and to join this internationalcollaboration. This is one of the goals of thelattice QCD of journal club.In the summer 2007, PNC focus group hassupported 3 NTU graduate students to attendthe INT summer school on lattice QCD(http://www.int.washington.edu/PROGRAMS/07-2b.html) at University of Washington. Our3 graduate students also received supportsfrom INT to cover their local expenses at theschool. This is the first time our graduatestudents to attend international summer schooland also to receive financial supports from theorganizing institution. In the future, we willencourage more Ph.D. students to participatethe renowned summer/winter schools in highenergy physics, e.g., TASI, Les Houches,ERICE, etc. Obviously, these schools willprovide excellent trainings to our students.Also, their interactions with other participantsat the schools will be an invaluable experienceto them.decays in the next-to-leading orderperturbative QCD formalism. With anenhancement of the color-suppressed treeamplitude and possibility of a new CPphase in the electroweak penguin, we canaccount better for the data of the direct andmixing-induced CP asymmetries in the B -> K pi, phi K and rho K decays. Ourproposal provides a possible resolution tothe well-known puzzles observed by the Bfactories. [Wei-Shu Hou , Hsiang-nan Li ,Satoshi Mishima, Makiko Nagashima,Phys.Rev.Lett.98:131801,2007].Fig. 4th generation effect on CP asymmetriesB. Observation of Direct CP ViolationThe obersevation of direct CP violation inB-> K+- pi-+ and finding the difference ofCP violating asymmetry between B-> K+pi-+and B+- -> K+- pi0. The figures belowillustrates the difference between decayrates of B meson and its anti-particle. [S.W.Lin et al (Belle Collab.)"Observation ofdirect CP violation in B -> K pi decays",submitted to Nature, 2007.]IV. Highlights of Research ResultsA. 4-th Generation Effects on CPasymmetriesWe study the effect from a sequentialfourth generation quark on penguindominatedtwo-body nonleptonic B mesonC. Cosmic microwave backgroundWe present the full set of power spectra143 ‹‹- Highlights of Programs

of cosmic microwave background (CMB)temperature and polarization anisotropiesdue to the coupling between quintessenceand pseudo-scalar of electromagnetism.This coupling induces a rotation of thepolarization plane of the CMB, thusresulting in a non-vanishing B mode andparity-violating TB and EB modes. Usingthe BOOMERANG data from the flight of2003, we derive the most stringentconstraint on the coupling strength. We findthat in some cases the rotation-induced Bmode can confuse the hunting for thegravitational lensing-induced B mode.[Guo-Chin Liu , Seokcheon Lee , Kin-Wang Ng , Phys.Rev.Lett.97:161303,2006.]D. Topological Susceptibility in QCDWe determine the topologicalsusceptibility (χ t ) in two-flavor QCD withexact chiral symmetry. The topologicalcharge density is unambiguously definedon the lattice using the overlap-Diracoperator which possesses exact chiralsymmetry. Simulations are performed on a16 3 32 lattice at lattice spacing ~0.12 fm atsix sea quark masses ranging m s ~ m s /6with ms the physical strange quark mass. Inthe small mq regime, our result of χ t isproportional to m q as expected from chiraleffective theory. Using the formula χ t =m∑/N f , we obtain the chiral condensate inQCD. [T.W. Chiu et al., talk at Lattice2007; S.Aoki et al.(JLQCD and TWQCDCollaboration), submitted to PRL].V. Selected Publications[1] Wei-Shu Hou, Hsiang-nan Li, SatoshiMishima, Makiko Nagashima, Fourthgeneration CP violation effect on B ---> Kpi, phi K and rho K in NLO PQCD. Phys.Rev. Lett. 98:131801 (2007).[2] Kuang-Ta Chao, Xiao-Gang He, Jian-PingMa, Comment on 'Chiral suppression ofscalar glueball decay', Phys. Rev. Lett.98:149103 (2007).[3] Kuang-Ta Chao Xiao-Gang He, Jian-PingMa, Comment on 'Chiral suppression ofscalar glueball decay', Phys. Rev. Lett.98:149103 (2007).[4] Xiao-Gang He, Jusak Tandean, G.Valencia, Does the HyperCP Evidence forthe Decay Sigma --> p mu+ mu- Indicate aLight Pseudoscalar Higgs Boson, Phys.Rev. Lett. 98:081802 (2007).[5] JLQCD and TWQCD Collaborations (H.Fukaya et al.), Two-flavor lattice QCDsimulation in the epsilon-regime with exactchiral symmetry, Phys. Rev. Lett.98:172001 (2007).[6] JLQCD and TWQCD Collaborations (H.Fukaya et al.), Two-flavor lattice QCD inthe epsilon-regime and chiral RandomMatrix Theory, Phys. Rev. D76:054503(2007).[7] TWQCD Collaboration (Ting-Wai Chiu etal.), Beauty mesons in lattice QCD withexact chiral symmetry. Phys. Lett.B651:171-176 (2007)[8] Jiunn-Wei Chen, Eiji Nakano, Shearviscosity to entropy density ratio of QCDbelow the deconfinement temperature.Phys. Lett. B647:371-375 (2007)[9] Cheng-Wei Chiang, Yu-Feng Zhou, FlavorSU(3) analysis of charmless B mesondecays to two pseudoscalar mesons, JHEP0612:027 (2006).[10] Yu-Chun Chen, Chung-Wen Kao, Shin-Nan Yang, Is there model-independentevidence of the two-photon-exchangeeffect in the electron-proton elasticscattering cross-section? Phys. Lett.B652:269-274, (2007).Highlights of Programs -›› 144

Focus Group on StringsCoordinator: Jen-Chi Lee (National Chiao tung University; email: jcclee@cc.nctu.edu.tw)Committee members: Chuan-Tsung Chan (TungHai University), Chiang-Mei Chen (National Central University),Choon-Lin Ho (TamKang University), Pei-Ming Ho (National Taiwan University),Hsien-Chung Kao (National Taiwan Normal University), Feng-Li Lin (National Taiwan Normal University)I. Brief Descriptionhe active member of string focusgroup include: Makoto Narita (Nat'lTaiwan Univ.), Shunsuke Teraguchi(Academic Sinica), Dan Tomino (Nat'l TaiwanNormal Univ.), Toshihiro Matsuo (Nat'lTaiwan Normal Univ.), Wen-Yu Wen (Nat'lTaiwan Univ.), Syoji Zeze (Nat'l TaiwanUniv.), Furuuchi Kazuyuki (Nat'l TaiwanUniv.), Dmitry Orlov (Nat'l Central Univ.), YiYang (NCTS), Peter Matlock (Nat'l ChiaoTung Univ.) and around 10 graduate students.The purpose of forming the string FocusGroup is to bring together string theorists inTaiwan and to encourage mutualcollaborations to enhance their researches.Currently, the regular group activities includeweekly seminars, mini-workshops andlectures. Some of them are given by invitedvisitors overseas. For the last few years, someresearch topics in our group are: AdS/CFTstring duality and its applications, noncommutativegeometry, string black hole,string cosmology and high energy stringscatterings.II. Research Activities1. Weekly string seminars at NTU:http://www.phys.ntu. edu.tw/string/index.htmThis is the main regular activity which wasstarted in 1996. Participants (15 to 20) frommany institutes including AS, NTNU, NCU,NCTS and NCTU come to attend the seminarevery Friday. The seminar lasted for two hoursso that people can have time enough to askquestions and learned how to work on aparticular subject. After the seminar, therewere many discussions of the audiences withthe speaker as well as with each others. Manyideas and collaborations came out of thesediscussions.2. Biweekly high energy seminar at NTNU:http://home.phy.ntnu. edu.tw/~highenergy/In addition to string theory, this seminarincludes topics such as cosmology and particlephysics so that people working at differentfields can communicate with each others.There are five string faculties and postdocs atNTNU which constitute one of the main stringresearch group at Taiwan. Many foreignvisitors visiting NTU stayed some days onNTNU campus and gave talks there.Some string seminars at NCU and Hsinchuwere arranged occasionally in joint name withlocal regular high energy physics seminars.String theorists from these areas wereencouraged to attend seminars held at Taipei.3. Mini-workshop on AdS/QCD:Recently there is much research interest onthe applications of String/Gauge duality. Oneof them is the AdS/QCD, the so called Sakai-Sugimoto model. Prof. Sugimoto was invitedto visit Taiwan early this year in March. Inpreparation of his visit, the string group held a2-day mini-workshop on this current researchtopic in February. All speakers were localresearchers and the aim was to educateourselves and learned the subject from eachothers. It turns out that these activities end upwith many collaborated papers on this subjectpublished in many honorable journals bymembers of the group (see section IV).145 ‹‹- Highlights of Programs

III. Visitors and InternationalCollaborationsFor the last few years, string focus groupcontinued to attract many foreign scientists tovisit Taiwan. Many of them were impressed byour active research activities and theenthusiasm of our group members. Some ofthem even brought their own grants to visit usand gave seminars here. The majority of themare Japanese visitors from prestigiousinstitutes such as Tokyo University, KyotoUniversity and YITP.1. For the last year, Chiang-Mei, Feng-Li andChuan-Tsung were supported by a NSCTaiwan-Japan exchange program to visitmany institutes in Japan. Before thisprogram was approved by NSC onTaiwanese side, there was a 3-year mutualexchange program supported by theJapanese organization "Koryu Kyokai"under the direction of Prof. Takeo Inami(Chuo U.). The financial support of thestring focus group also helped facilitate thevisits of scientists from Japanese side, andmuch collaboration has been initiated sincethen. Early this year, Jen-Chi Lee and YiYang were supported by NSC and NCTU tovisit Tokyo University. Many connectionsand possible future collaborations werefurther initiated. Besides, after four yearpostdoc research here at Taiwan, one of ourmembers, Dr. Shunsuke Teraguchi, is goingto take an assistant professorship at NagoyaUniversity in Japan.Some collaborations between Taiwan andJapan have been set up due to these mutualvisits. To name some, recently Pei-Ming hada joint paper with Prof. Yutaka Matsuo ofTokyo University, Choon-Lin (Tam-KangUniversity) had many joint papers withProf. Ryu Sasaki of YITP and Jen-Chi andYi have set up a collaborated project withProf. Tamiaki Yoneya of Tokyo University.There are also many on-going collaboratedprojects among postdocs on both sides.2. In addition to the Japanese visitors, anotherimportant connection we have is Prof.Chong-Sun Chu of Durham University inUK. He is actually the person who initiatedthe exchange program of Taiwan and Japan.He has also been helping us to invite manyforeign visitors and organize activities inTaiwan. He has been making strong effort tohelp scientists in Taiwan and to collaboratewith us. We have benefited a lot from him.In fact, one of our member, Hsien-ChungKao, was visiting Chu at Durham for thelast academic year.Last year, Prof. Chu had joint papers withPei-Ming and with Feng-Li. Another projectis being set up recently with Jen-Chi and Yi.3. A joint paper on BPS bubbling solution inIIB supergravity of Prof. James Liu fromUniversity of Michigan and Feng-Li andWen-Yu was published recently.IV. Highlights of Research Results1. High Energy String Scatterings:This is a long term project which wasstarted in 2003 based on many earlier works ofJen-Chi in 90's. Following a breakthrough ofChuan-Tsung and Jen-Chi in 2003, Taiwangroup has published more than 15 papers onthis single subject (about 10 of them are inNucl. Phys.B), and about half of the groupmembers participated in the project. Althoughthese works have not well recognized yet, theyare truly initiated in Taiwan, and it is hopedthat they will eventually attract moreinternational attention in the near future. In thelast year, Chuan-Tsung, Jen-Chi and Yi, andJen-Chi and Yi generalized the linear relations(stringy symmetry) to D-brane. Moreimportantly, Jen-Chi and Yi have shown thecoexistence of the linear relations and thesofter exponential fall-off behavior of highenergy string scattering amplitudes. Currently,together with Prof. Yoneya of TokyoUniversity, Jen-Chi and Yi are trying to fittheir results to Yoneya's "space timeuncertainty relation'. Pei-Ming and his studentalso published a paper on this subject last year.Publications[1] Jen-Chi Lee and Yi Yang, Linear Relationsand their Breakdown in High EnergyMassive String Scatterings in CompactHighlights of Programs -›› 146

Spaces, 0705.1872, To be published inNucl. Phys. B (2007).[2] Jen-Chi Lee and Yi Yang, Linear relationsof high energy absorption/emissionamplitudes of D-brane, hep-th/0612059,Phys. Lett. B646, 120 (2007).[3] Jen-Chi Lee, Zero-norm states andsuperstringy symmetries,hep-th/0610272(to be published by World Scientific).[4] Chuan-Tsung Chan, Jen-Chi Lee and YiYang, Power-law behavior of stringsscattered from domain-wall at highenergies and breakdown of their linearrelations, hep-th/0610219 (2007)[5] Chuan-Tsung Chan, Jen-Chi Lee and YiYang, Scatterings of massive string statesfrom D-brane and their linear relations athigh energies, hep-th/0610062, Nucl. Phys.B764, 1-14 (2007)[6] Chuan-Tsung Chan, Jen-Chi Lee and YiYang, Notes on High energy limit ofBosonic closed string scatteringamplitudes, hep-th/0604122, Nucl. Phys.B749, 280 (2006).[7] Pei-Ming Ho and Xue-Yan Lin, Linearrelations among 4-point functions in thehigh energy limit of string theory, Phys.Rev. D73, 126007 (2006).2. AdS/CFT Duality and its ApplicationsRecently there is much interest on theapplications of String/Gauge duality. TheNTNU group, led by Feng-Li, has publishedseveral papers in this topic. Two papers are onnull-like cosmology's dual SYM, one is on thejet-quenching in AdS/QCD with chemicalpotential, and one is to systematicallyconstruct the BPS bubbling solution in IIBsupergravity. Another one is on the Hagedornstrings in AdS space. Wen-Yu and EijiNakano, Shunsukei and Wen-Yu alsopublished two papers on studying severalobservable quantities in RHIC (RelativisticHeavy Ion Collider) based on the AdS/QCD,the so called Sakai-Sugimoto model.Publications[1] Feng-Li Lin, Toshihiro Matsuo, DanTomino, Hagedorn Strings andCorrespondence Principle in AdS(3),arXiv:0705.4514 (2007)[2] Bin Chen, Sera Cremonini, AristomenisDonos, Feng-Li Lin, Hai Lin, James T.Liu, Diana Vaman and Wen-Yu Wen,Bubbling AdS and droplet descriptions ofBPS geometries in IIB supergravity,arXiv:0704.2233 (2007)[3] Feng-Li Lin, Dan Tomino, One-loop effectof null-like cosmology's holographic dualsuper-Yang-Mills, JHEP 0703:118 (2007).[4] Feng-Li Lin, Toshihiro Matsuo, JetQuenching Parameter in Medium withChemical Potential from AdS/CFT, Phys.Lett. B641:45-49 (2006).[5] Feng-Li Lin, Wen-Yu Wen,Supersymmetricnull-like holographic cosmologies, JHEP0605:013 (2006).[6] W. Y. Wen, Note on deconfinementtemperature with chemical potential fromAdS/CFT, arXiv:0707.4116 (2007).[7] E. Nakano, S. Teraguchi, W. Y. Wen, Dragforce, jet quenching, and AdS/QCD, JHEP0610, 055 (2006).3. International Collaborated Papers[1] Pei-Ming Ho, Yutaka Matsuo, A Toymodel of open membrane field theory inconstant 3-form flux, hep-th/0701130(2007).[2] Chong-Sun Chu, Pei-Ming Ho, TimedependentAdS/CFT duality and nullsingularity, JHEP 0604:013(2006).[3] Bin Chen, Sera Cremonini, AristomenisDonos, Feng-Li Lin, Hai Lin, James T. Liu,Diana Vaman and Wen-Yu Wen, BubblingAdS and droplet descriptions of BPSgeometries in IIB supergravity,arXiv:0704.2233 (2007)[4] Yeuk-Kwan E. Cheung, KonstantinSavvidy, and Hsien-Chung Kao, GalaxyRotation Curves from String Theory, astroph/0702290(2007).[5] Non-local matching condition and scaleinvariantspectrum in bouncing cosmology,147 ‹‹- Highlights of Programs

Chong-Sun Chu, Ko Furuta, Feng-Li LinPhys.Rev.D73:103505, (2006).[6] Choon-Lin Ho and Ryu Sasaki, DeformedFokker-Planck Equations, condmat/0612318(2006).[7] Choon-Lin Ho and Ryu Sasaki, Deformedmulti-variable Fokker-Planck Equations,cond-mat/0703291 (2007).[8] Choon-Lin Ho and R. Sasaki, QuasiexactlySolvable Fokker-Planck Equations,arXiv:0705.0863 (2007)[9] V.R. Khalilov, Choon-Lin Ho, Scattering ofSpin-polarized Electron in an Aharonov-Bohm potential, arXiv:07083131 (2007)[10] C.-M. Chen, D. V. Gal'tsov and D. G.Orlov, Extremal black holes in D=4Gauss-Bonnet gravity, Phys. Rev. D75,084030 (2007).4. Talks presented at InternationalConferences[1] Pei-Ming Ho, Infinite Symmetries in thehigh energy limit, talk presented at String2006, Beijing, China, June 19-24, 2006.[2] Jen-Chi Lee, Zero-norm States andSuperstringy symmetries, talk presented atXXXIII International Conference on HighEnergy Physics (ICHEP06), Moscow,Russia, July 26-Aug 2, 2006. hepth/0610272.(to be published by worldscientific)[3] Jen-Chi Lee, Linear Relations and theirBreakdown in High Energy StringScatterings, talk presented at InternationalEurophysics Conference on High EnergyPhysics (EPS2007), Manchester, England,July19-25, 2007. arXiv:0705.1872. (to bepublished by Journal of Physics:Conference Series)[4] Hsien-Chung Kao, Second orderPerturbative Calculation of QuasinormalModes, talk presented at 13th InternationalSymposium on Particles, Strings andCosmology, London, UK, July 2-7, 2007.Note: Some publications listed in this report may notacknowledge the support of NCTS. We apologize forthe ignorance of some members of the group whoforgot to put it on the papers. Those works areresearch results under the support of NCTS.Highlights of Programs -›› 148

Highlights of ProgramsInterdisciplinary FieldsFocus Group on Atomic PhysicsCoordinator: Daw-Wei Wang (National Tsing Hua University; email: dwwang@phys.nthu.edu.tw)Committee members: Ying-Cheng Chen (Academia Sinica), Chung-Hou Chung (National Chiao Tung University),Shin-Chuan Gou (National Changhua University of Education), Dian-Jiun Han (National Chung Cheng University),Tsin-Fu Jiang (National Chiao Tung University), Jiang-Nan Liu (Fu-Jen Catholic University),Yi-Wei Liu (National Tsing Hua University), Wen-Chin Wu (National Taiwan Normal University)I. Brief Descriptionroup size:Active faculty members are about 20,including experimentalists.Goal:1) encourage more cooperation betweenfaculty in this community, includingcooperation between theorists andexperimentalist. 2) attract moreresearchers/students to join to form a stableresearch environment. 3) enhance the researchquality by actively cooperating withinternational frontier researchers andconcentrating on some promising projects.Research direction:Our FG encourage the following fourdirections of research:(1) Strongly correlated effects in coldatoms: This is a new team formed by somejunior faculty from condensed matterbackground. Besides of the analytic methodsdeveloped in many-body theory, some of usalso developed several advanced numericaltools for strongly correlated systems, likeQuantum Monte Carlo, Density MatrixRenormalization Group, and DynamicalMeanfield Theory etc. We will also explore theexotic many-body phases of cold atom systemsas well as the dynamical and finite temperatureproperties.(2) Weakly interacting Bose gases: Acertain portion of our group members havedeveloped their own numerical technique tostudy the static as well as the dynamicproperties of Bose-Einstein condensation ofcold atoms in the mean-field level. Severalanalytic work on the transition temperatureproperties of interacting bosonic atoms as wellas magnetic dipoles are also developed.(3) Atomic structure theory: We have had agood start in atomic structure theory in the pastfew years when Prof. Tu-Nan Chang (USC,USA) was in Taiwan as NCTS director. Wewill keep such cooperation on-going andencourage more national-wide activities in thissubfield.(4) Intensive laser and plasma: Although sofar there are not many theoretists in this newfield in Taiwan, there has been some greatprogress in the experiments in AcademiaSinica and NCU recently. We hope this groupcan grow larger and stronger by cooperatingwith local experimentalist as well as some149 ‹‹- Highlights of Programs

oversea researchers, like Chii-Dong Lin (UKS,USA), regularly.II. ActivitiesSummer School:From 8/20-8/24 in 2007, we held the 4 thAMO summer school in National Tsing HuaUniversity. Different from the style in previousyears, this time we select a specific topic:Condensed matter theory in ultracold atoms tohighlight the important and main stringresearch direction. The course was organizedfrom atom cooling to BEC-BCS crossover andcold molecules. There are more than 100students to join and the feedback was verygood. This is also a good training for thosewho have been in this field.Local Workshop:On 9/7-9/8 in 2007, we held AMOworkshop in Tung Hai University. The goal ofthis workshop is to provide a flexible forumfor domestic physicists working in AMOphysics and other related fields as well as tohelp initiate possible collaborations betweenparticipators. We had a very flexible timeschedule to encourage speakers and otherresearchers to discuss the potential researchdirection and related problems in details.Several ideas are exchanged and discussed forfuture cooperation.International Workshop:We are planning to hold one internationalworkshop in the end of 2008 or early of 2009on some specific topics of cold atoms (forexample, dipolar atoms/molecules), which areclosely related to the interest of localresearchers and main string development.Seminar/Journal Club:We are going to host two bi-weekly (ormonthly) seminars, one in National Tsing HuaUniversity and one in National ChanghuaUniversity of Education, to serve differentlocal researchers in different locations. Thegoal is to update the most important researchand enhance cooperation between students aswell as faculty.III. Visitors and InternationalCooperationVisitor:We invite Prof. Jianping Yin at the physicsdepartment and key laboratory of spectroscopyof East China Normal University in Shanghaifrom Aug. 8 to 15, 2007. During his visit inTaiwan Prof. Jianping Yin had intensediscussions with local researchers (especiallyYing-Cheng Chen and Dian-Jiun Han) in thefields of cold atoms and molecules, atom andmolecule optics, etc. both in theory andexperiment. This visit stimulates hiscollaboration with the local scientists in thefuture and, as we expected, will have apositive impact on the local related researchfields.Visitors in the near future:1) We also have invited Prof. T.-L. Ho(Ohio State University, USA) to visit Taiwanin the end of Nov. of 2007. Prof. Ho is aworld-wide famous theorist in systems ofultracold atoms and he is very willing to knowmore about the local research in the relatedfield in Taiwan. We expect his visit will form aclose connection with people in stronglycorrelated systems. 2) We have invited Prof. C.Greene (Director of JILA, USA) to visitTaiwan for at least one week in May 2008. Weexpect that Prof. Greene's coming will broadenthe horizon of local research in atomicstructure, atomic scattering and systems ofultracold atoms.International cooperation:Our group members have activeinternational cooperation with frontierresearchers. For example, Daw-Wei Wang(National Tsing Hua University) recently has apaper with Prof. P. Zoller in Innsbruck, todevelop a new scenario for dipolar latticestructure. Prof. Ying-Jer Kao (National TaiwanUniversity) cooperated with Prof. A. Sandvik(BU) in the development of quantum MonteCarlo calculation. Prof. Tsin-Fu Jiang(National Chiao Tung University) developed anew numerical method for high intensity laser,cooperating with Prof. Chii-Dong Lin (KansasState University). Prof. Te-Kuei Fang worksHighlights of Programs -›› 150

with Prof. Tu-Nan Chang (USC) in atomicstructure theory, etc. Results of thesecooperation have been or will soon bepublished.IV. Highlight of Research ResultsStrongly interacting cold atoms/molecules:A. Exotic quantum phases of polar molecules:Daw-Wei Wang and his cooperatorsinvestigate the quantum phase transitions ofbosonic polar molecules in double layer [1]and multi-layer systems [2]. This work hasbeen presented in academic institutes likeYale, NIST, KITP, Maryland, Stuttgart andInnsbruck etc. Recently Prof. Wangcooperated with Prof. P. Zoller to develop adipolar lattice system, which has beensubmitted to Phys. Rev. Lett.B. Supersolid phase in square optical lattice:Ying-Jer Kao and his cooperators study theground state phases of the boson-Hubbardmodel using quantum Monte Carlomethods. They observe supersolids withcheckerboard, striped, and quarter-filledcrystal symmetry, when the system is dopedaway from commensurate fillings. Thiswork has been submitted to Phys. Rev. Lett.C. Incommensurate supersolid phase intriangular lattice: Chung-Hou Chung andhis cooperators study the ground statephases of the the Bose-Hubbard model inan anisotropic triangular optical lattice withspecial emphasis on the supersolid phase.They find a possible "quasiincommensurate"supersolid phase in thethermodynamic limit. This work has beensubmitted to Phys. Rev. Lett.Weakly interacting bosonic atoms:A. Statistical mechanics of weakly interactingbosons: Tsin-Fu Jiang and Yee-Mou Kaodeveloped a two-fluid theory to study thefractional change of Bose-Einsteincondensation transition temperature due tothe trap potential, the finite number ofparticles, and the mutual atomicinteractions. They also explored thepeculiar structure for the systems of dipolarGases. [3, 4]B. Vortex ring in BEC: Shin-Chuan Gou andhis cooperators study the quantized vortexring is a 3-dimensional structure of solitarywaves having the shape of "smoke ring"that is formed by closing the core of avortex line upon itself. They developanalytic solutions of the vortex ring motionand other related properties in a semiclassicalmanner. [5]C. Collective mode of BEC: Wen-Chin Wu andhis student have used a modified Gaussiandistribution to study the physical propertiesof one and two-component ultracold atoms[6]. Jiang-Nan Liu and his cooperator applythe hyperspherical (HS) method to study aBEC in quasi-2D free space stabilized andconfined under the influence of anoscillating magnetic field. Analysis of thestationary state solutions shows that thehyperspherical single-particle densityexhibits certain characteristic scalingdependence on energy akin to the Townessoliton [7]Atomic structure and spectroscopy:Te-Kuei Fang and Tu-Nan Chang haverecently employed a B-spline-based complexrotation (BSCR) method with spin-dependentinteraction to study atomic photo-ionizationfor two-electron and divalent atoms. Theirpreliminary results are in good agreement withthe observed spectra. [8]High intensity laser theory:An essential modification to the kernel inthe calculation of hydro-genic momentumwave functions in finite space is developed byTsin-Fu Jiang and his cooperators, using only afew hundreds grid points the modificationallows eigenvalues accurate to about 10 -7 . Thismethod can be applied to general diatomicmolecule with single-active-electron (SAE)under laser pulse, too.V. Support AMO experimentalistsWe invite Prof. Jianping Yin to help theexperimental setup of Prof. Ying-Cheng Chen151 ‹‹- Highlights of Programs

(IAMS, Academia Sinica) and Prof. Dian-JiunHan (National Chung Cheng University).Besides, we also support a student of Prof.Chin-Chun Tsai (National Cheng KungUniversity) to present their current nice workin Cs spectroscopy measurement in aninternational conference [9]. We believe aclose connection between theoreticaldevelopment and the local experimentalobservation is necessary.VI. Selected Publications[1] D.-W. Wang, Quantum phase transitions ofpolar molecules in bilayer systems, Phys.Rev. Lett. 98, 060403 (2007).[2] D.-W. Wang, M.D. Lukin, and E. Demler,Quantum fluids of self-assembled chains ofpolar molecules, Phys. Rev. Lett. 97,180413 (2006).[3] Y. M. Kao and T. F. Jiang, Transitiontemperature of a weakly interacting Bosegas, Phys. Rev. A 73, 043604 (2006)[4] Y. M. Kao and T. F. Jiang, Transitiontemperature of the interacting dipolar Bosegas, Phys. Rev. A 75, 033607 (2007).[5] T.-L. Horng, S.-C. Gou and T.-C. Lin,Bending-wave instability of a vortex ringin a trapped Bose-Einstein condensate,Physical Review A 74, R041603 (2006)[6] C.-C. Huang and W.C. Wu, Using modifiedGaussian distributions to study the physicalproperties of one- and two-componentultracold atoms, Phys. Rev. A 75, 023609(2007).[7] C.N. Liu, T. Morishita and S. Watanabe,Time-dependent hyperspherical studies fora two-dimensional attractive Bose-Einsteincondensate, Phys. Rev. A 75, 023604(2007).[8] T.K. Fang and T.N. Chang, B-spline-basedcomplex-rotation method with spindependentinteraction, Phys. Rev. A, 76,012721 (2007).[9] Wei-Xiang Chen, Ray-Yuan Chang, Thou-Jen Whang, Chanchal Chaudhuri, and C.C. Tsai, The third and fourth 1 g states ofNa2: A pair of twins, Chem. Phys. Lett.439, 29 (2007).Remarks: [1,2] are stimulated in a mini-workshop of AMOfocus group workshop, [3-6,8] are by the financial andadministrative support of NCTS, [7] is also initiated inthe discussion during AMO workshop, and [9] aresupported for the international conferencepresentation.Highlights of Programs -›› 152

Focus Group on Quantum Information SciencesCoordinator:Yueh-Nan Chen (National Cheng Kung University; email: yuehnan@mail.ncku.edu.tw)Hsi-Sheng Goan (National Taiwan University; email: goan@phys.ntu.edu.tw)Committee members: Yia-Chung Chang (Academia Sinica), Pochung Chen (National Tsing Hua University),Chi-Yee Cheung (Academia Sinica), Chung-Hsien Chou (National Cheng Kung University),Li-Yi Hsu (Chung Yuan Christian University), Chopin Soo (National Cheng Kung University),Zheng-Yao Su (National Center for High-Performance Computing),Wei-Min Zhang (National Cheng Kung University)I. Introductionhe main mission of the QIS focusgroup is to build a platform ofcommunication and discussion for researchersin this area in Taiwan. In the last few years, wehave brought QIS researchers in Taiwan towork and discuss research together and to holdactivities, such as scientific seminars,workshops and short-term schools. We havealso been seeking to establish links andexchanges as well as to initiate collaborationswith other QIS researchers worldwide.Focused research topics: Quantumdecoherence, quantum computation, quantummeasurement, quantum entanglement andcommunication.II. Activities and Beneficiaries• Activities1. Summer school on, "Non-equilibriumdynamics and quantum coherence" atNCKU, July 4 ~ 6 (2007).2. Winter school and workshop on, "QuantumInformation Science", January 4 ~ 6 (2008).3. Seminars at NCKU and NTU.• Beneficiaries1. Ever since Prof. B. L Hu (Univ. ofMaryland) became the senior multi-yearvisitor of our focus group, one of the majorQIS focus group research topics wasfocused on the field of quantumdecoherence. The 2007 summer school on"Non-equilibrium dynamics and quantumcoherence" suggested by Prof. Hu was thesecond summer school (the previous oneheld in 2006) focusing on this particulartopic. It attracted many participants (~70),including faculties, postdocs and students.The participants and QIS focus groupmembers benefited much from the twosummer schools. As a result of the summerschools, several focus group members haveengaged in the research on "Non-Markoviandynamics of qubits and continuous variablesystems in external environments". Somepreliminary results have come out and somehave been published (or to be published).2. We also successfully attracted youngresearchers and new graduate students intothis field, such as the postdoctoral fellows(Dr. M. T. Lee and Dr. J. H. An) andgraduate students (Mr. W. Y. Tu, Mr. H. B.Chen, Mr. D.B. Tsai, Mr. C.H Li and Mr.Y.Y. Lai).• Training of young-generation physicists1. Financial supports for internationalconferences(1) Dr. Ming-Tsung Lee (NCKU)-- HCIS15 at Tokyo(2) Dr. Che-Ming Lee (NCTU)-- Young European Physicists meeting2007153 ‹‹- Highlights of Programs

(3) Mr. Wei-Yuan Tu (NCKU)-- 4 th APWQIS at Singapore2. Inviting potential young-generationphysicists as speakers at summer school(1) Dr. Ming-Tsung Lee (NCKU)(2) Mr. Son-Hsien Chen (NTU)(3) Mr. Ming-Hao Liu (NTU)(4) Mr. Tu-Wei Yuan (NCKU)focus on non-Markovian dynamics ofquantum dot qubits.2. Prof. G. J. Milburn at the University ofQueensland and Prof. Xin-Qi Li at theChinese Academy of Science-- With Prof. H.-S. Goan on quantummeasurement and quantum feedbackcontrol of qubits and continuous variablesystems.III. Visitors and InternationalCollaborations• Visitors1. Prof. B. L. Hu, Univ. of Maryland, USA(Jan. 2007 and July 2007)-- Collaboration with Prof. C. H. Chou onNon-Markovian dynamics of qubits2. Prof. S. A. Gurvitz, Weizmann Institute,Israel (Nov. 2007 ~ Jan. 2008)-- Collaborations with Prof. W. M. Zhang,Prof. H. S. Goan, and Prof. Y. N. Chen onQuantum measurement and quantumtransport3. Prof. Zhanjun Zhang, Anhui University,China (Oct 2006 ~ Oct. 2007)-- Collaboration with Prof. W. M. Zhang onQuantum cryptography4. Dr. Neil Lambert, Univ. of Tokyo, Japan(Nov. 2007)-- Collaboration with Prof. Y. N. Chen onQuantum transport and shot noise5. Mr. Lukas Gilz, Univ. of Kaiserslautern,Germany (Aug. 2007 ~ Sep. 2007)-- Collaboration with Prof. Y. N. Chen onRetardation effect between qubits6. Mr. Yeong-Cherng Liang, University ofQueensland, Australia (Sep. 2007)• International Collaborations1. Prof. T. Brandes at Technische UniversitätBerlin, Germany-- A three-year international collaborationproject with Prof. Y. N. Chen. MainlyIV. Highlights of Research Results• Research results1. Quantum computationA. Charge-to-spin conversion of electronentangled states and spin interaction freesolid-state quantum computing:We have proposed an implementationof scalable spin quantum computation insemiconductor nanostructure withoutresorting to spin-spin interaction. [1].The techniques of single electrontransitions and the nanostructure ofquantum-dot cellular automata (QCA)are used to generate charge entangledstates of two electrons, which are thenconverted into spin entanglement statesusing single spin rotations only.Deterministic two-qubit quantum gatesare also manipulated using only singlespin rotations with the help of QCA.B. Geometric phase quantum computing:By collaborating with Prof. Oh's groupin Singapore, a scheme for implementingunconventional geometric quantumcomputation by using the interaction oftwo atoms with a two-mode cavity fieldhas been proposed. [2]2. Dynamical decouplingWe develop a numerical framework toinvestigate the renormalization of thenon-Markovian dynamics of an openquantum system to which dynamicaldecoupling is applied. Our resultsindicate that the renormalization of thenon-Markovian dynamics criticallyHighlights of Programs -›› 154

depends on the spectral density of theenvironment and the envelope of thedecoupling pulses. It also opens a newavenue to further optimize thedecoupling via pulse shaping. [3]3. Shot-noise spectrums of non-Markovianquantum dot excitonsWe propose to detect non-Markoviandecay of an exciton qubit coupled tomulti-mode bosonic reservoir via shotnoisemeasurements. Non-equilibriumcurrent noise is calculated for a quantumdot embedded inside a p-i-n junction. Anadditional term from non-Markovianeffect is obtained in the derivation ofnoise spectrum. [4]4. Quantum electromechanical systemsWe have investigated to use a circuitQED cavity [5] as a motion transducer toprobe the properties of a quantumelectromechanical system (QEMS).5. Quantum entanglement andcommunicationA. Decomposing the Lie Algebra su(N)An algebraic structure, the quotientalgebra, universally embedded in the Liealgebra su(N) is discovered. [6] In thisstructure, the Lie algebra su(N) ispartitioned into a certain number ofabelian subalgebras or vector subspaces,each of which is considered anindividual element. This structureenables systematic and exhaustivedecompositions for the Lie algebra, suchas a fast scheme for the Cartandecomposition. The applications of thiswork include design of optimal quantumgates, classification of quantumentanglement, analysis of quantumcontrol and others.B. Mixed States with an Incomplete Set ofStabilizer GeneratorsWe investigate a family of mixedentangled states with common stabilizersamong the mixtures of the correspondingdensity matrix. [7] The non-locality ofthese mixed entangled states can beverified by the maximal violation ofstabilizer-based Bell-type inequalities.• Invited presentations1. Science seminar at Max. Planck. Institute,Dresden, GermanyProf. Y. N. Chen, Title: Entanglement andteleportation via superradiance2. 4 th Asia Pacific conference on quantumInformation ScienceProfs. W. M. Zhang, C.-Y. Chueng, H.-S.Goan, and Mr. W.-Y. Tu.3. International Workshop on QuantumDynamics and Biomolecular Function,Yeppoon, QLD, AustraliaProf. H.-S. Goan4. Seminar at the University of Queensland,Brisbane, AustraliaProf. H.-S. GoanV. Publications[1] Free spin quantum computation withsemiconductor nanostructures, Wei-MinZhang, Y. C. Wu, M. Feng and C. P. Soo,quant-ph/0502002 (submitted to Phys. Rev.Lett. with a revised version, 2007).[2] Unconventional geometric quantumcomputation in a two-mode cavity, C. Wu,Z. Wang, X.-L. Feng, H.-S. Goan, L.C.Kwek, C.H. Lai and C.H. Oh, Phys. Rev. A76, 024302 (2007).[3] Dynamical decoupling-inducedrenormalization of non-Markoviandynamics, Pochung Chen, Phys. Rev. A 75,062301, (2007).[4] Super-Poissonian noise of quantum dot p-injunction, Y. N. Chen, Appl. Phys. Letts.90, 162114 (2007).[5] A microwave transducer for a nanomechanical resonator, G. J. Milburn, C. A.Holmes, L. M. Kettle and H.-S. Goan,cond-mat/0702512.[6] A Scheme of Cartan Decomposition forsu(N), Z. Y. Su, quant-ph/0603190.155 ‹‹- Highlights of Programs

[7] Mixed entangled states with two or morecommon stabilizers, L. Y. Hsu, Phys. Rev.A 76, 022322 (2007).[8] Electron transport of a driven three-levelsystem in an asymmetric double quantumdot irradiated by an external field, Y. Y.Liao, D. S. Chuu, and Y. N. Chen, Phys.Rev. B 75, 125325 (2007).[9] Non-Markovian reduced dynamics andentanglement evolution of two coupledspins in a quantum spin environment, X. Z.Yuan, H.-S. Goan and K. D. Zhu, Phys.Rev. B 75, 045331(2007).[10] Non-Markovian entanglement dynamicsof quantum continuous variable systemsin thermal environments, K.-L. Liu andH.-S. Goan, Phys. Rev. A 76, 022312(2007).[11] Influence of an external magnetic field onthe decoherence of a central spin coupledto an antiferromagnetic environment, X.Z. Yuan, H.-S. Goan and K. D. Zhu, NewJ. Phys. 9, 219 (2007).[12] Studies on the electronic and vibrationalstates of colloidal CdSe/ZnS quantumdots under high pressures, C. T. Yuan, Y.C. Lin, Y. N. Chen, Q. L. Chiu, W. C.Chou, D. S. Chuu, W. H. Chang, H. S.Lin, R. C. Ruaan and C. M. Lin,Nanotechnology 18, 185402 (2007).[13] Entanglement detection via the conditionof quantum correlation, C. M. Li, L. Y.Hsu, Y. N. Chen, D. S. Chuu, and T.Brandes, accepted by Phys. Rev. A(2007).[14] Secure Quantum Bit Commitment UsingUnstable Particles, C. Y. Cheung,International Journal of Modern PhysicsB (in press, 2007).[15] Detection inefficiencies in Cabello's proofof the three-qubit Bell theorem withoutinequalities, Li-Yi Hsu and Jau-HanChen, Phys. Letts. A 364, 101 (2007).[16] Generation of entangled photon pairs bysemiconductor quantum dots in astructure of quantum cellular automata,M. Feng, J. H. An, and W. M. Zhang, J.Phys.: Condens. Matter 19, 326215(2007).Highlights of Programs -›› 156

Highlights of ProgramsPlasma Science ProgramCoordinator: Kuan-Ren Chen (National Cheng Kung University; email: chenkr@mail.ncku.edu.tw)Committee members: Lin-Ni Hau (National Central University), Jang-Yu Hsu (National Cheng Kung University),Chwung-Shan Kou (National Tsing Hua University), Wei-Chih Liu (National Taiwan Normal University),Jyhpyng Wang (Academia Sinica)I. Descriptionhe NCTS Plasma Focus Group wasrecommended to become a workinggroup because NCTS believed that localplasma research is not so focused. By mutualagreement with Div. Head H. N. Lee, theNCTS Plasma Science Program was formed inthis February. The Program identifies thefollowing plasma research frontiers: space andastrophysical plasma, fusion plasma, laserplasma, surface plasma, coherent radiation,plasma applications, low temperature plasma,and gluon plasma. The local community hasresearch activities in all but the last one. Infact, it has world-leading research result inalmost every area, although the size of localplasma physics community is still small.Education is essential for this community toincrease its enabled manpower and futureprosperity. Plasma researches are often acrossdisciplinary boundaries and important in bothscientific frontiers and critical applications.The NCTS Plasma Science Program isexpected to provide a forum for the localplasma science community, to achieve thefollowing objectives, and to operate under theguidelines listed below.1. Objectives:A. Promoting theoretical plasma research inTaiwan.B. Stimulating research collaborations withexperimentalists, of inter-disciplinary, andbeyond national boundaries.C. Incubating young generations of plasmascientists.2. Guidelines:1. Following the NCTS written guidelines.2. Providing the needed administrativeassistances and a flexible and reliable servicefor easy budget access. 3. The NCTS budgetshould be used efficiently. 4. Suggestions foractivities and positions are encouraged. 5.Proposal and report in written should be brief;in most cases, an email may be enough as longas key information and justifications included.6. The program committee makes the decisiononly based on the objectives, the guidelines,the academic merit, and available budget. 7.Activities aiming to stimulating collaborationand interaction are encouraged and have ahigher priority for budget supporting. 8.Activities aiming to incubating younggenerations are encouraged and have a higherpriority for budget supporting. 9. Sponsoredforeign visitors should be superior in particular157 ‹‹- Highlights of Programs

methodology and knowledge. 10. Localexperts and groups are encouraged to offertutorial courses, schools, and workshops. 11.Self-organized working groups acrossinstitutions are encouraged. 12. Each workinggroup should have focused interest andactivities, and is encouraged to be boundedwith specific experimental concerns. 13. Theplasma sub-areas and working groups arecoupled through common interest insimulation and theory, such as nonlineardynamics.? 14. Anyone in the community iswelcome to participate in any of the groups ofhis/her interest.II. Activities1. Surface Plasma Working Group MeetingsSurface plasma on metallic surface is anewest frontier in plasma research. It is aresearch area of multi-disciplines, involvingphysics, mathematic, electro-optics, biomedical,electronics, materials, nanotechnology,mechanical, and electricalengineering. This biweekly meeting wasorganized by Professor Y. C. Lan in 2006 andProfessor S. J. Chen in 2007. Activeparticipants include five NCKU professors andone professor with Kaohsiung Univ. ofApplied Science and their students. In additionto working group discussion, external andinternal speakers are invited. The purpose is toeducate students and to stimulatecollaboration. In this July, NCKU realized theimportance of a simulation result by the group.A NCKU experimental team supported by theTop University fund is formed and a joinedbiweekly meeting is being held. The numberof involved professors is increased to aboutfifteen.2. Computational Plasmonic Nano-PhotonicsMeetingsAt nano scale, charge is the most effectivemedia to interact with photons. Thus, for manyexperts, plasmonic is the most important areaof nano-photonic research. While coveringboth fundamental physics and applications,this monthly working group meeting aims tounderstand the interactions of photons andmetallic/dielectric structures, and toinvestigate novel optical phenomena. Abouttwo speakers per month are invited forpresentation. It is organized by Professors D.P. Tsai of NTU and W. C. Liu of NTNU. Theorganizers and some of its participants havesuccessfully landed a National Nano Project.3. Laser-Plasma Interaction Summer SchoolA. PurposeIn Taiwan and possibly many other placesin Asia, it is not uncommon to meet aprospective graduate student who is interestedin experimental sciences but poorly preparedfor laboratory work. Many students can dotextbook exercises well, but do not know howto describe the thread of a screw, or how toread the color code of a resister. They cannotoperate a milling machine or a soldering iron,or tell the difference between epoxy andsilicon rubber. The reason is simple: these arenot part of their education or experience. Inthis summer school held at National TaiwanUniversity by Jyhpyng Wang of AcademicSinica from July 16 to 20, we wish to extendtheir education in this direction, even though itis not possible to provide them a reallaboratory experience.B. CoursesForty hours of lectures that form fourteencourses were delivered. The objective is tointroduce to the participating students a nearcomplete set of basic knowledge that isrequired in a laser-plasma laboratory. Inaddition, recognizing computer simulation as aform of numerical experiments, the coursesalso cover basic knowledge of computersimulation. The courses are: characteristicsand applications of optical components,ultrafast optics and high-power lasers, basiclaser-plasma interaction, experimentaltechniques in laser-plasma interaction, basicnumerical simulation, Particle-in-cellsimulation, handy computation: Introductionto Matlab, Mathematica, and Mathcad,working with electronics, computer control ofinstruments, introduction to electro-opticsinstruments, working with vacuum, dataanalysis and curve fitting, mechanical designHighlights of Programs -›› 158

and drafting, data plotting and presentation,and using LaTeX for preparing scientificdocuments.C. ParticipationThere are 160 participants enrolled. Inadditional to a few faculties and some fulltimeresearch assistants, most of them aremaster students, undergraduate students, andPh.D. students. At the end, we have conducteda poll to see how students evaluate the courses.In the poll we asked students to rate eachcourse in two scales, one on the level ofdifficulty and the other on the pace oflecturing. The cost per participant is about1,500NT for this five days intensive school.4. Particle-in-cell Mini-schoolParticle-in-cell is a first-principle and themost powerful method to simulate plasmas.Aiming to educate students and young plasmascientists in a joined effort, this mini-schoolbrings local experts together. It is organized byProfessor Y. C. Lan and will be held at NCKUon September 29 and 30.III. Visitors and InternationalCollaborations1. Professor Liu Chen, UC Irvine, USAProfessor Liu Chen visited NCTS from11/8-26, 2006. He spent the first week inNCU, the second week in NCKU, and then inNDHU and NCU. In addition to giving serieslectures on gyrokinetic theory and toroidalphysics, he started the collaboration on thework of relativistic ion cyclotron instabilityunder non-uniform magnetic field withProfessor K. R. Chen and student, Mr. T. H.Tsai. After his visit, Mr. Tsai went to UCIrvine at the end of March 2007 to carry outthe theoretical derivation, under the support ofNational Science Council. It is expected forMr. Tsai to stay there till January 2007.During the meantime, Professor Liu Chen hasvisited Taiwan twice (one in July and the otherin September) and discussed with Professor K.R. Chen, under the support of NCU with aChair Professorship. Preliminary result yieldedis consistent qualitatively with Particle-in-cellsimulation; the quantitative comparison isbeing done. The three are expected to gettogether for in-depth discussion in Novemberduring the annual meeting of Plasma PhysicsDivision of American Physical Society, held atOrlando, FL, USA.2. Professor C. M. Ryu, Postech, KoreaProfessor C. M. Ryu visited NCTS from6/26 to 7/8, 2007. He is a well rounded plasmaphysicist and has done research in variousareas of plasma physics.? He madepresentations on "Magnetic Field Generated byTransport Flow" at both NCKU and NCU.During the visit, he started collaborative workwith Professor J. Y. Hsu on the spheromakplasma equilibrium. He pointed out thecorrelation dimension to quantify the fractaldimension and one student has implemented anumerical code successfully to examine forexample the Henon map, and will apply thesame to arc root dynamics, and otherstochastic systems. The spheromak plasmaequilibrium paper while submitted to APSmeeting still needs further effort to finish,however.IV. Highlights of Research ResultsTaiwan's plasma physics community isrelatively small in size as compared with otherresearch fields of physics. However, theacademic performance is impressive and theinternational reputation is high. For example,in the areas of electron cyclotron maser, dustyplasmas, space plasma, laser plasma, red-Sprite observation, fast ion cyclotroninstabilities, and recently surface plasma,Taiwan's groups are making outstandingoriginal contributions and, in fact, are amongleaders of the international researchcommunity.There are many outstanding researchresults in the local plasma community. Due topage limitation, only one of the most recentadvances in surface plasma is introduced here.Diffraction, a general characteristic of wavephenomena, occurs whenever a wave frontencounters and propagates past an obstruction,has being studied since L. da Vinci in 1400s.159 ‹‹- Highlights of Programs

It sets a lower limit on the spot size of lightand thus the ultimate resolution of numerousdiagnostic and fabrication instruments. In fact,the diffraction limit inspired Heisenberg forhis uncertainty principle of quantummechanics; they can be deduced from eachother. A novel scheme with surface plasmaeffects is being studied to address thediffraction limit. The simulation results arebeing verified by experiments in both visiblelight and microwave frequency ranges. Thelight focusing process, besides its academicinterest, is expected to open up a wide range ofapplication possibilities; e.g., photolithographythat is the critical issue stopping the Moore'slaw of semiconductor industry.Highlights of Programs -›› 160

Research Activities of IndividualsResearch Activities on Spintronics and N-leg LaddersJudith E. Bunder (email: bunder@phys.cts.nthu.edu.tw)Postdoctoral researcher, 2003/11/12~2007/7/31n the past few years I have beeninterested in spintonic materials, andspecifically dilute magnetic semiconductors(DMS). In part a) I present a brief descriptionof my recent work on DMS-based magnetictunnel junctions. Another research interest isground-state properties and gapless excitationsin N-leg ladders. In part b) I discuss spinchargeseparation in N-leg ladders.a) Spin-polarized transport in dilutemagnetic semiconductor tunneljunctionsOne of my recent research interests istransport in magnetic tunnel junctions (MTJ)[1] which contain dilute magneticsemiconductors (DMS). A conventionalmagnetic tunnel junction usually consists of aninsulator between two ferromagnets, thoughany magnetic material can in principle be used.I was particularly interested in transport effectsin MTJ in which the magnetic materials areidentical except for their relativemagnetization orientations.A DMS is created by doping group III-Vor II-VI semiconductors with a transition metaland these impurity ions couple to the itinerantcarriers, giving the DMS some uniquemagnetic properties [2]. Experimental studieshave shown that using DMS as the magneticmaterial in a MTJ can provide quite a largetunneling magnetoresistance (TMR) such asalmost 300% in Ga(Mn)As/GaAs/Ga(Mn)Asat 0.39K [3]. Unfortunately, as most DMShave critical temperatures well below roomtemperature such large TMR in DMS-basedMTJ are only expected at extremely lowtemperatures, deceasing rapidly as thetemperature increases. However, this is nottrue for all DMS and some, such as GaNdoped with Mn and Cr, are known to havecritical temperatures above room temperature[4].To describe the variation in conductancewith temperature T and relative magnetizationorientation θ I define the function(1)where G(θ,T) is the conductance. This isrelated to the TMR byTMR=R(π,T)G(0,T)/G(π,T). The conductancewas evaluated using the Landauer formula [5]while the magnetization in the DMS wasdetermined from self-consistent Green'sfunctions [6]. Fig 1. and 2. show R(θ,T) for FigFig 1: The R(q,T) ratio for carrier concentration0.3 nm-3.161 ‹‹- Research Activities of Individuals

two different carrier concentrations in a MTJcontaining DMS Ga(Mn)As and insulatorAlAs. The shape of these curves with respectto the temperature resemble the shape ofitinerant carrier magnetization while theangular dependence is ~sin 2 (θ/2). This angulardependence agrees with what is observedexperimentally.Fig 2: The R(q,T) ratio for carrier concentration0.1 nm-3.The Julliere formula [1] may be used togive a semiclassical approximation of R(q,T),(2)where P is the polarization. Although thissemiclassical formula does give the correctangular dependence, the temperaturedependence is quite different to what Iobtained from the Landauer formula,especially for large carrier concentrationsindicating that the Julliere formula is not aparticularly good approximation.b) Spin-charge separation in weaklycoupled N-leg laddersIn a one dimensional chain it is known thatelectrons can separate into two components, aholon which carries the charge of the electronbut no spin, and a spinon which carries thespin of the electron but no charge. This is aphenomenon known as spin-charge separation[7]. A two-leg ladder, i.e., two identical onedimensional chains bound weakly together,does not have spin-charge separation [8].Together with Hsiu-Hau Lin I haveinvestigated whether or not spin-chargeseparation in N-leg ladders is limited to N=1.It is already known that odd and even leggedladders have quite different properties [9]. Forexample, the ground state of odd leggedladders at half filling belongs to the sameuniversality class as the single Heisenberg spinchain. They have long-ranged ferromagneticorder and gapless spin-wave excitations. Incontrast, the even legged ladders are all spinliquids with a spin gap. So, the possibility thatthe odd legged ladders would also resembleone-dimensional chains in their ability tosupport spin-charge separation was intriguing.We used a Hubbard Hamiltonian with onsiteinteractions. On solving therenormalization group flow equations we findthat the coupling constants obey severalgeneral rules which remain true for allparameter variations. In addition, thesecoupling constants always retain the same signwhich is a fair indication of an absence of aphase transition. Whether or not an N-legladder undergoes a phase transition has been indispute for some time.To proceed further we bosonize theHamiltonian, i.e., we map the fermion fields inthe Hamiltonian to boson fields [8]. We use anon-standard mapping of the boson fieldswhich gives a far simpler, albeit still complex,Hamiltonian than the standard mapping. Weuse the Hamiltonian to determine zero energygap excitations, i.e., when a set of boson fieldscan be changed by a specific amount withoutaffecting the Hamiltonian.Quantum numbers, such as the total chargeQ i and the total spin S i in the ith leg may bewritten in terms of the boson fields [8] andthen used to determine whether or not spincharge separation can exist in an N-leg ladder.If we can retain a constant Hamiltonian whenQ i =1 while S j =0 for all j then we have shownthat a particle with the same charge as anelectron but with no spin is permitted in theladder, i.e, there is a zero energy gap for thecreation of holons in the absence of spinons inthe ladder and therefore we have spin-chargeseparation. Alternatively, we could show thatS j = 1 / 2 while Q i =0 for all i. This latter casedescribes the existence of a spinon without aResearch Activities of Individuals -›› 162

holon so again would indicate spin-chargeseparation is possible.Our bosonized N-leg Hamiltonian remainsinvariant when N is odd and the central leg i chas charge Q ic =1 but S j =0 for all j. Thereforewe have shown that a holon can exist in thecentral leg of an odd legged ladder. The otherN-1 legs cannot support spin-chargeseparation. Even legged ladders have no spinchargeseparation. Thus we have shown thatspin-charge separation is not unique to onedimensionalchains.References[1] E. Y. Tsymbal, O. N. Mryasov and P. R.LeClair, J. Phys.: Condens. Matt. 15 R109(2003).[2] S. A. Wolf, D. D. Awschalom, R. A.Buhrman, J. M. Daughton, S. von Molnar,M. L. Roukes, A. Y. Chtchelkanova and D.M. Treger, Science 294, 1488 (2001).[3] D. Chiba, F. Matsukura and H. Ohno,Physica E 21, 966 (2004).[4] J. M. D. Coey. M. Venkatesan and C. B.Fitzgerald, Nature Mat. 4, 173 (2005).[5] Z. Zheng, Y. Qi, D. Y. Xing and J. Dong,Phys. Rev. B 59, 14505 (1999).[6] J. E. Bunder, S.-J. Sun and H.-H. Lin,Appl. Phys. Lett. 89, 72101 (2006).[7] C. Kim, A. Y. Matsuura, Z.-X. Shen, N.Motoyama, H. Eisaki, S. Uchida, T.Tohyama and S. Maekawa, Phys. Rev. Lett.77, 4054 (1996).[8] H.-H. Lin, L. Balents and M. P. A. Fisher,Phys. Rev. B 58, 1794 (1998).[9] S. White, R. Noack and D. J. Scalapino,Phys. Rev. Lett. 73, 886 (1994)163 ‹‹- Research Activities of Individuals

Research Activities on Interdisciplinary ResearchCheng-Hung Chang (Institute of Physics, National Chiao Tung University; e-mail: chchang@phys.cts.nthu.edu.tw)Center scientist, 2007/2/1~2009/1/31n the past year, I continue my study in(I) spintronics and (II) biophysics.Two topics in these two fields are highlightedbelow and the other are listed in thereferences.(I) SpintronicsThe semiclassical path integral (SPI)method has been successfully applied toexplain spin dynamics in several mesoscopicsystems under Rashba spin orbit interaction inour previous works. Examples include spincurrent transports through open quantum dotslike rings, Sinai billiards, and square billiards,spin relaxations in triangular billiard, circularbilliards, generalized Sinai billiards, andbilliards with rough boundary. This year weextend the application of this technique to spinrelaxation problems in quasi-1D channel ofnarrow width w. Experimentally this systemhas been studied in Awschalom's grouprecently, where several interesting andunexplained questions have been addressed[PRL 97, 036805 (2006)]. By applying SPImethod, our recent work Ref. [1] (i) confirmsthe experimental relaxation time in large widthregime and explains the reason for thesaturation in small width regime, (ii) gives aslowdown onset of spin relaxationapproximately the same as the experimentvalue, (iii) theoretically derives andnumerically confirms the Bessel-function spinrelaxation in a quasi-1D impurity-free channel,and (iv) confirms the linear dependence of therelaxation rate versus width square predictedrecently [PRB 61, R2413 (2000)]. The SPImethod again proved itself to be a powerfulapproach to understand the spin dynamics ofsystems with spin-orbit interaction.Fig. 1 The spin relaxation time τ S of [1,0,0] sample (bluecircle) and [1,1,0] sample (green star) versuschannel width w are obtained from Awschalom'sexperiments (n-doped InGaAs). The τ S calculatedfrom the SPI method are the red diamond and theblack triangle curves, taken from different fittingfunctions. The inset demonstrates three examplesof spin polarization relaxation for channel width (a)w=1µm, (b) w=1.8µm, and (c) w=12µm.(II) BiophysicsBeing able to introduce bioactive moleculessuch as DNA, proteins or chemical reagentsinto living cells and then examine theconsequent responses is critical to theadvancements of modern biology. Certaincompounds are readily "membranepermeable", they can enter the cells by simplediffusion. On the other hand, delivery ofmembrane impermeable molecules to livingcells or tissues can be achieved by a variety ofchemical, physical, or biological methods.Each technique has its own advantages anddrawbacks. In general, molecular delivery canbe better done in relatively undifferentiatedrather than differentiated cells. Cell lines aremore effective targets for transfection thanResearch Activities of Individuals -›› 164

primary cultured cells or tissue explants andproteins are more difficult to be delivered intocells than DNA. In Ref. [5] we contrive a newmolecular bombardment method to tacklesome of these challenges.References[1] Cheng-Hung Chang, Hui-Fen Lo, A.G.Mal'shukov, Semiclassical path integralapproach on spin relaxations in quasi-1Dwires, (preprint).[2] W.-M. Huang, C.-H. Chang, and H.-H. Lin,Non-collinear magnetic junction mediatedby Rashba interaction, J. Magn. Magn.Mater. 310, e759 (2007).[3] T.Y. Tsong and C.-H. Chang, A Markovianengine for a biological energy transducer:The Catalytic Wheel, Biosystems 88, 323(2007).[4] W. H. Kuan, C. S. Tang, and C. H. Chang,Spectral properties and magneto-opticalexcitations in semiconductor double ringsunder Rashba spin-orbit interaction, Phys.Rev. B, 75, 155326 (2007).[5] W.-N. Lian, C.-H. Chang, Y.-J. Chen, R.-L.Dao, Y.-C. Luo, J.-Y. Chien, S.-L. Hsiehand C.-H. Lin, Intracellular delivery can bemediated by bombarding cells or tissueswith accelerated molecules or bacteriawithout the need for carrier particles, Exp.Cell Res. 313, 53 (2007).[6] C.-H. Chang and T.Y. Tsong, Energytransduction in molecular machines, toappear in Nano (2007).Fig. 2 (A and B) The ratio of cells containing moleculesdelivered by bombardment (orange bars), bydiffusion for 1 min (pink bars), or 10 min (blue bars)was calculated. (Bottom plot) The hypothetic modelfor the molecular bombardment assay. Molecules insmall water droplets (blue dots) are accelerated bythe high-pressure gas and used to bombard thecells. The combination of wave front and plasmamembrane penetration by high speed moleculescauses some of the affected cells (cells #2 and #3,but not cell #1) to become transiently permeable tonon-accelerated molecules (red dots) added to themedium, allowing their entry by diffusion. Themembranes reseal within 10 min after thebombardment.165 ‹‹- Research Activities of Individuals

Research Activities on Quantum Transport and MeasurementYueh-Nan Chen (Department of Physics, National Cheng-Kung University; email: yuehnan@mail.ncku.edu.tw)Center scientist, 2006/10/13~2008/10/12y research is mainly on the theory ofquantum transport and measurement.There are three major results in the past year:Super-poissonian noise in a quantump-i-n junctionI investigated theoretically the shot-noisespectrum of a quantum dot p-i-n (ptype/intrinsic/n-type)junction (Fig. 1)Effect from the nonrelativistic cutofffrequency of the exciton decay may berevealed with the feature of super-poissoniannoise without making the Markovianapproximation (Fig. 2). To become practicallyobservable in experiments, high qualityquantum well or quantum dot arrays, whichexhibits superradiance, in a p-i-n junction issuggested to enhance the zero-frequency noise(Fano factor).Electron transport of a driven threelevelsystem in an asymmetric doublequantum dotWe investigated Electron tunneling througha three-level system in an asymmetric doublequantum dot irradiated by an external field(Fig. 3).Fig.1 Energy-band diagram of a QD inside a p-i-n junction.Fig. 2 Shot-noise spectrum of QD excitons in a p-i-njunction. Sub-poissonian noise represented by theblack line is the result of Markovian approximation.Super-poissonian noise (red and blue lines) is theconsequence of non-Markovian effect. To plot thefigure, the exciton spontaneous lifetime (=1/γ) usedhere is 1.3ns, and the cutoff frequency for blue(red) line is 9x 10 16 (1.2x 10 17 )Hz. Inset: Noiseincreased by the enhancement of the effectivedipole moment (400 times) via superradiance.Fig.3 Schematic view of a three-level system whichconsists of the ground state in the left dot, theground state and first excited state in the right dot ina double quantum dot device. An external fieldirradiates on the device and leads to the transitionbetween two states in the right dot.For a resonant external field, twosymmetric peaks occur in the currentspectrum. If the field frequency is detuned,unequal contributions from two channels leadto two asymmetric peaks with populationinversion, which can be observed with theincreasing of Rabi frequency. On the otherhand, as the ground states in two dots areResearch Activities of Individuals -›› 166

equal, a suppression of current occurs aroundthe resonant frequency. In contrast, anenhanced behavior is found for the case ofunequal ground states.ground states.Fig.5 PL peak positions as a function of applied pressuresFig.4 Current as a function of energy difference ∆εbetween two ground states for different Rabifrequencies. The inset shows the currents IR (dashedcurve) and Iε (dotted curve) for γ=5Γ.Studies on the electronic andvibrational states of colloidalCdSe/ZnS quantum dots under highpressureIn addition to the theoretical works, I alsocollaborated with the experimental group inNational Chiao-Tung University. We studiedthe electronic and vibrational states ofcolloidal core/shell CdSe/ZnS quantum dots atroom temperatures by using high pressureoptical measurements. Pressure dependentquadratic lattice behavior can be observedclearly from photoluminescence (PL) andRaman spectras up to ~7 GPa. This quadraticrelationship is consistent with theoreticalprediction. The average pressure coefficientsfor PL and Raman measurements, as well asdeformation potential are 32 meV/GPa , 4.2cm -1 and -1.69 eV, respectively.References[1] Yueh-Nan Chen, Appl. Phys. Lett. 90162114 (2007).[2] Y. Y. Liao, D. S. Chuu, and Y. N. Chen,Phys. Rev. B. 75, 125325 (2007).[3] C. T. Yuan, Y. C. Lin, Y. N. Chen, Q. L.Chiu, W. C. Chou, D. S. Chuu, W. H.Chang, H. S. Lin, R. C. Ruaan, and C. M.Lin, Nanotechnology 18, 185402 (2007).167 ‹‹- Research Activities of Individuals

Research Activities on Particle Physics PhenomenologyKingman Cheung (Department of Physics, National Tsing Hua University; email: cheung@phys.cts.nthu.edu.tw)Center scientist, 2007/11/1~2009/10/31I joined the Center as a CenterScientist on November 2006. I amalso the convener for the focus group on"Collider, Astroparticle and BSM". You mayfind some materials here the same as thoselisted under the focus group. My research areais in particle physics phenomenology.IntroductionThe upcoming LHC is the place for thenext big discovery. More than half of theresources in high energy community will beput into it. Together with other plannedcosmology experiments, testing new ideasbeyond the standard model (SM) will be themajor activities in the next 10-20 years. Myrole is to link up theory and experiments. Inpast years, I have accomplished a number ofworks on supersymmetry, Higgs physics, extradimensions, and other new physics. I madepredictions for the most interesting features ofsome well-motivated models, such as splitsupersymmetry, large extra dimensions,unparticle, etc. In addition, I also madeinterpretations for some anomalous results inexperiments, including the muon anomalousmagnetic moment, pentaquarks, quark-leptoncomplimentarity, etc. They will be some of themost important physics topics at the LHC. Inthe following, I highlight two topics that I feelvery exciting.A twist in the search for the HiggsbosonThe title of the paper is "Role of h ➝ ηη inthe search of intermediate-mass Higgs bosonat the Large Hadron Collider", authored byKingman Cheung, Jeonghyeon Song, and Qi-Shu Yan, published in Physical Review Letters[1]. The paper consists of a well-motivatedstudy and the result is very important to futuresearch for the Higgs boson at the LHC.The Higgs boson decay mode into twopseudoscalar bosons (h ➝ ηη) plays the roleof relieving the so-called little hierarchyproblem and easing the tension between theLEP2 Higgs boson mass bound and theprecision data. However, the emergence of h➝ ηη decay mode has undesirable effects onthe golden search modes (h ➝ γγ,ηη) of theHiggs boson at the LHC. This is because whenthe branching ratio B(h ➝ ηη) increases to 0.7(in order to solve the little hierarchy problem),the branching ratio B(h ➝ ηη) goes down toabout 0.25 and B(h ➝ γγ) will go down by afactor of 4 or more. This will significantlyworsen the chance of detecting anintermediate-mass Higgs boson at the LHC.The LHC may not be able to find the Higgsboson if the two-pseudoscalar decay modedominates. Our Letter explicitly shows that theassociated production of the Higgs boson witha W or Z boson can recover the loss ofsensitivity in the golden modes. With theHiggs boson decaying into two pseudoscalarbosons, which further decay into 4 b jets,together with at least a charged lepton from theW or Z boson decay, a significant Higgs bosonsignal is observable at the LHC. We found thatthe invariant mass spectrum of the 4 b-taggedjets (shown in the figure) can beautifullydistinguish the Higgs signal peak from thecontinuum background. One can alsoreconstruct the mass of the Higgs boson aswell as the mass of the pseudoscalar boson.Since the ultimate goal of the LHC is huntfor the Higgs boson, which is responsible forelectroweak symmetry breaking and massgeneration, our work fully establishes thefeasibility in searching for the intermediatemassHiggs boson if h ➝ ηη dominates andsolves the little hierarchy problem.Research Activities of Individuals -›› 168

Figure 1: Invariant mass spectrum M 4b of the signal andvarious backgrounds for the bench-mark point Bof the NMSSM.Novel signals in unparticle physicsThis is a current hot topic in particlephysics. We have finished two papers on thesubject. There are at least two more works arein progress. The first paper is a Letter,authored by Kingman Cheung, Wai-YeeKeung, and Tzu-Chiang Yuan, and has beenpublished in Physical Review Letters [2]. ThisLetter communicates very interesting resultsthat are useful to other researchers taking upthe challenge in unparticle physics.We have also written a comphrensive paperon the subject, which is also published inPhysical Review D [3]. The paper listed theformalism, derivations, and the results forimportant phenomenology of unparticle. Webelieve that the paper will be well cited anduseful to others.The subject is about the scale invariance or,in broader terminology, conformal invariance.Our existing particle theory is not conformalinvariant, as the invariance is obviouslybroken by all the discrete masses of particles.Banks and Zaks in the 80s showed that anumber of supersymmetric field theoriescontain a conformal window such that thetheories can develop IR fixed points, where thescale is invariant.Recently, perceived by Georgi a scaleinvariant sector (coined unparticle) with a nontrivialinfrared fixed point at a higher energyscale may actually describe the real world athigh energy. So he visualized what kind ofphysics that such a sector can induce in highenergy phenomenology. The unparticle with ascale dimension d U can be interpreted as acollection of d U invisible massless particles,which can be unveiled by measurements ofvarious energy distributions in the processes Z➝ U and e - e + ➝ – > γU at e - e + colliders,as well as mono-jet production at hadroncolliders.The new results of our Letter are that notonly we work out the most important channelsto observe unparticle effects at high energycolliders, but also we discover the novelpropagator effect of the unparticle.The novel features, induced by scaleinvariance, include effective 4-fermioninteractions and a nontrivial phase factor,which interferes with the SM amplitudes in aninteresting manner The spectacular phasefactor exp(–id U π) associated with thepropagator in s-channel can give rise to nontrivialbehavior in a number of processes. Westudied the effects in the Drell-Yan processand in the one-loop muon anomaly. In thefigure, we show the fractional difference fromthe standard model prediction around the Zpole. Interesting interference pattern can beseen clearly.Figure 2: Fractional difference from the SM prediction ofthe Drell-Yan invariant mass spectrum for2various at the Tevatron in units of λ 1 .References[1] K. Cheung, J. Song, and Q.-S. Yan, Phys.Rev. Lett. 99, 031801 (2007).[2] K. Cheung, W.-Y.Keung, and T.-C.Yuan, Phys. Rev. Lett.99, 051803 (2007).[3] K. Cheung, W.-Y.Keung, and T.-C.Yuan, Phys. Rev. D76,055003 (2007).169 ‹‹- Research Activities of Individuals

Research Activities on Cosmic Acceleration and Dark EnergyJe-An Gu (email: jagu@phys.cts.nthu.edu.tw)Assistant research scholar, 2006/8/1~presenty research is focused on the cosmicacceleration and dark energy. Thecosmic acceleration at the present epoch is oneof the most mysterious phenomena. Itsexistence was first suggested in 1998 by typeIa supernova (SN Ia) data, and was furtherreinforced recently by updated SN Ia data andWMAP measurement of cosmic microwavebackground (CMB). Most of the explanationsfor this mysterious phenomenon invoke someexotic energy source, as generally called "darkenergy", which provides significant negativepressure and repulsive gravity to drive theexpansion to accelerate. However, both theexistence of the cosmic acceleration and theneed to invoke dark energy as the origin aremodel dependent and should be seriouslyquestioned and carefully investigated.Our current knowledge about the cosmicacceleration is very limited. We just realizethat the current observational results indicatethe present universe is undergoing anaccelerating expansion which is defined in theFLRW cosmology, a simplified cosmologicalmodel. In reality, i.e., regarding the realsituation of our universe, we do not knowwhether the observational results reallysuggest the existence of the cosmicacceleration, corresponding to which thedefinition of acceleration for the evolution of aspace is an essential issue. In addition, we donot know in our real universe whether theinhomogeneities can generate the cosmicacceleration and explain the observationalresults (in particular, the SN Ia data), orintroducing dark energy (or other exoticsources) is necessary.In my research, in one way I investigate thepossibility of generating acceleratingexpansion via inhomogeneities, and in theother way I study possible natural ways ofgenerating small cosmological constant (ordark energy) which by assumption isresponsible for the cosmic acceleration.I. InhomogeneityIn this topic I try to answer twofundamental questions: 1. Is the FLRWcosmology a good approximation? 2. Caninhomogeneity generate acceleration?Regarding the first fundamental question,via perturbative analysis it was shown byIshibashi and Wald in 2005 that the correctionon the Einstein equations contributed from theperturbations to the background RW metric isnegligible under some conditions for theperturbations, and therefore FLRW is a goodapproximation. However, regarding long-time,large-scale phenomena such as the cosmicevolution, the validity of perturbative analysisis doubtful and whether the conditions invokedtherein fit the real situation of our universeneeds further check.In my work I followed the sameperturbative approach while keeping severalterms involving time and spatial derivatives. Ifound that, opposite to the result mentionedabove, the contributions from the perturbationsmay be significant when the perturbations varyviolently in space-time (i.e. with regard tohigh-frequency or large-wave-number modes).Regarding the second question, we foundexamples of accelerating expansion based onthe Lemaitre-Tolman-Bondi (LTB) solution,which is an exact solution of the Einsteinequations for a spherically symmetric dustfluid. These examples illustrate the strongcorrelation between acceleration andinhomogeneity. These results strongly supportthe suggestion that inhomogeneity can induceacceleration. These counter-intuitiveacceleration examples also give us a hint aboutResearch Activities of Individuals -›› 170

how our understanding of the interplay ofgravity and the space-time evolution(including the cosmic evolution) may gowrong. They open a new perspective forunderstanding the cosmic evolution.II. Dark Energy and HierarchyRecent observations imply that dark energyis likely to be a cosmological constant withvacuum energy density ρ DE ~ (10 –3 eV) 4 . If darkenergy is indeed a cosmological constantwhich never changes in space-time, then itmust be a fundamental property of the spacetime.This would then introduce a new energyscale, 10 –3 eV, which is 15 orders of magnitudesmaller than the Standard Model scale, M SM ~TeV.There has been another long-standinghierarchy problem in physics, i.e., theexistence of a huge gap between the Planckscale M Pl of quantum gravity at 10 19 GeV andthat of the standard model gauge interactionsat TeV, by a factor ~ 10 16 , which is roughly atthe same order of the above-mentionedhierarchy.This surprising numerical coincidencebetween these two energy gaps prompts us tothe wonder whether these two hierarchyproblems are indeed related (in a fundamentalway). In our work we suggest that the sameRandall-Sundrum (RS) brane-world setup toaddress the hierarchy problem about theweakness of gravity (i.e. why M Pl >> M SM ) mayalso address the smallness problem of thecosmological constant. Relying on thisconnection as our guidance, we explore thepossibility of interpreting the Casimir energydensity induced in a SUSY-breaking braneworld as the cosmological constant, with theobserved value of dark energy as a reference.Invoking the RS warp geometry and Higgsgravitinocoupling onthe TeV brane forSUSY-breaking, wedemonstrate that the4D Casimir energy onthe brane indeedscales as TeV 2 / M Pl ,remarkably, just rightfor the dark energy.171 ‹‹- Research Activities of Individuals

Research Activities on Atomic PhysicsHung-Cheuk Ho (email: hcho@phys.cts.nthu.edu.tw)Postdoctoral researcher, 2006/5/16~presenty current interest is mainly in themany-body perturbation theory(MBPT) calculation of atomic structure ofheavy atoms. Ongoing projects includerelativistic third-order MBPT calculation ofthe hyperfine structure (hfs) constants ofCesium-133.Experimentally, the 6 2 P 3/2 state hf splittingof 133 Cs has been measured accurate to fivesignificant figures by Gerginov et al. [1] Thisaccuracy enabled the first determination of anon-zero magnetic octupole moment of 133 Cs in2003. Ref. [1] is a combined experimental andtheoretical study of hfs of the 6 2 P 3/2 state of133Cs. Its calculation is based on an all-ordermethod. And to our knowledge, this is the onlyrelativistic many-body calculation of the hfsconstant c reported for this case. In this regard,it would be very interesting to perform adifferent hfs calculation to compare with boththeir measurement and computation.We are extending our previous work of hfsstudies of 133 Cs. [2] In that work, we evaluatedthe off-diagonal hfs matrix element betweenthe 6 2 P 1/2 and 6 2 P 3/2 states, and the constant afor the 6 2 P 3/2 state. Now, we calculate the hfsconstants b and c for the electric quadrupoleand magnetic octupole couplings. Particularcare has to be taken for the nuclear chargedistribution, because the constant c is verysensitive to the charge distribution (the radialintegrand in c depends on r -4 ). Therefore, themore sophisticated Fermi nuclear distributionis used.The following table shows a comparison ofrecent reported values of 133 Cs 6 2 P 3/2 hfsconstants in MHz:As shown in the table, the two set ofexperimental hfs constants a and b differ, butthe constants c agree within uncertainty. Thetheoretical values are also in disagreementwith measurement. The calculation of a in Ref.[2] is a third-order one, while those of Ref. [4]is an all-order single-double with partial triple(SDpT) one. The 5% difference between thesetwo values is probably due to the differentnuclear charge distributions used, and the factthat gauge-invariant RPA matrix elements areused in Ref. [2], but not in Ref. [4].Precise hfs calculations for heavy alkalimetalatoms are of particular interest, as theyprovide a check for the accuracy of atomicwavefunctions. Highly accurate wavefunctionsare required for atomic parity nonconservation(PNC) calculations. Our group's work on PNCis in progress.References:[1] V. Gerginov, A. Derevianko, and C.ETanner, Phys. Rev. Lett. 91, 072501(2003).[2] W.R. Johnson, H.C. Ho, and C.E Tanner,Phys. Rev. A, 70, 014501 (2004).[3] D. Das and V. Natarajan, Europhys. Lett.72, 740 (2005).[4] M.S. Safronova, W.R. Johnson, and A.Derevianko, Phys. Rev. A, 60, 4476(1999).[5] R.K. Chaudhuri and C. Sur, arXiv:physics/0406083v1 (2004).a b c50.28827(23) [1] -0.4934(17) [1] 0.00056( 7) [1]50.28163(86) [3] -0.5266(57) [3] 0.00087(32) [3]48.51 [4] 139Q (b)* [1] 0.00068Ω (bxµ N )[1]51.09 [2] -0.559 [5]* The value of the nuclear quadrupole moment Q used toobtain b is not specified.Research Activities of Individuals -›› 172

Research Activities on Condensed Matter PhysicsWen-Hsuen Kuan (email: whkuan@phys.cts.nthu.edu.tw)Postdoctoral researcher, 2006/2/1~presentecently, my research interests aremainly focusing on two fields: Bose-Einstein Condensation and Spin-Orbit Effecton Low Dimensional Semiconductor QuantumStructures. The main research results achievedduring this year are as follows:I. Analysis of instabilities and thebreakdown of superfluidity ofBose-Einstein condensates inoptical latticesThe observation of superfluid flow in theweakly interacting Bose gas has the systemserved as an ideal paradigm for understandingsuperfluidity. The existence of a criticalvelocity in BEC cloud also verifies Landau'sargument on the phonon generation and theonset of instabilities in the superfluid He-4.Such a loss of superfluidity was investigatedexperimentally by studying the dynamics ofBECs in a periodic optical potential. 1 Burgeret. al. showed that when the velocity of thecondensate is lager than the sound velocity, thefraction of atoms remaining in the superfluidpart decreases, showing the evidence of theonset of Landau instability. The superfluiddiminishes when the condensate travels fasterand interacts strongly with the lattice. Weclaim that the condensate might enter into thedynamical instability regime where thenumber of quasiparticles grows exponentiallythus to impart energy into the flow and destroythe superfluid. In this regime, Bogaliubou deGennes approach to the description ofsuperfluid dynamics breaks down.To confirm our arguments and demonstratethe collective flow of BECs, we simulate thedynamics of BECs in a quasi-1D shallowoptical lattice. Atoms in the superfluid parttraveling with the group velocity via k.papproximation. The group velocity thatdeduced from the dispersion of the bandstructure is described by a macroscopicenvelope function, which can be obtained bysolving the effective-mass-Gross-Pitaevskiiequation. By applying small perturbations onthe system, the dynamics of the condensate isinvestigated via the exploration of collectiveexcitation spectrum. Different from analyses inNiu's works, 2 we provide an unified theory ofLandau and dynamical instabilities in opticallattices. 3 In addition to the phonon excitation,our theory shows that the generation of lowenergy antiphonons plays the crucial role onthe dissipation of superfluid. 4 It can beunderstood as follows: In the unidirectionalflow, the counter-motion of phonons andantiphonons should be governed by theDoppler effect such that the contributions onthe excitation spectrum differ quantitatively.The numerical simulation within Landauinstability regime fits quite well with theexperimental results in Ref. 2. However, theconsistency close to the dynamical instabilityregime is still lacking. To revise thediscrepancy, we propose to considerperturbations on the condensate with negativeeffective mass. We expect a power-low likededuction of the fraction of superfluid atomscan be reached if the life time of the unstablecondensate is long enough to be observed.Before the collapse of the superfluidcondensate, cold atoms may have thepossibility to locate at a metastable state ifthere is a local minimum in the potentialenergy functional. Otherwise, the condensatemay undergo a macroscopic quantumtunneling 5 to the dense state where the twobodydipolar collision and three-body inelasticcollision occur frequently. We apply theinstaton technique and variational method toinvestigate the decay mechanism. By usingsum rules in the estimation of collectivemodes, the bounce exponent shows a five-173 ‹‹- Research Activities of Individuals

fourth power relation to the condensatenumber. Evaluations and competitions ondecay rates of the mentioned routes are alsotaken at finite temperatures. 6II. Dipolar Bose-EinsteinCondensation beyond BornapproximationRecently attained BEC gas of highlymagnetic chromium atoms shows a signatureof dipolar interactions. 7 This opens a door forinvestigations on the dynamics of cold atomsin strong electric field under which the longrange dipole-dipole interaction may haveprofound effect. Moreover, it provides a betterunderstanding on the formation of the BECmolecules and the mechanism in BEC-BCSphase transition.Yi and You 8 first introduced apseudopotential approach for describingslowly moving particles interacting via shortrangecontact potential and the long-rangedipolar force. However, their approach basedon first Born approximation (FBA) that validonly in the low energy scattering regime. Theweak interaction assumption breaks down nearscattering resonances. Therefore, it is crucialto develop a full many-body theory for dipolebeyond FBA.In the recent work of Wang, 9 the firsteffective many-body theory that is capable todescribe bosonic dipolar condensates evennear the shape resonance (SR) or in thestrongly interacting regime has been derived.Using the scattering matrix elementscalculated by Deb et. al. 10 the dipolar effectnear SR is found to be significantlyrenormalized so that the system becomes morestable than what is predicted using simpleFBA. Moreover, the elementary excitation ofthe 2D condensate behaves as q in the longwavelength limit, showing the same lowenergy physics as 2D charge bosons withCoulomb interactions.The effective Hamiltonian beyond FBA in3D has been derived, and the ground stateenergy is calculated by using the Gaussiantype trial wave function. However, it isinadequate to do so while the condensateprofile is highly anisotropic. We expect thatthe dipolar Gross-Pitaevskii equation can beexactly solved in a fully numerical calculation.We propose to use the Monte Carlo integrationmethod in dealing with a many-dimensionalcalculation. Eventually, the optimal set ofparameters of trial wave functions can bedetermined via the variational method in thesort of the lowest energy solution.III. Rashba and Dresselhaus spinorbitinteractions on the spectralproperties, magneto-opticalexcitations, and generation of dcspin currents in low dimensionalsemiconductor quantumstructuresRecently, applications on spin-orbitinteraction (SOI) originated from the breakingof inversion symmetry that gives rise tointrinsic spin splitting in semiconductorsystems open a field of spintronics. It waspointed out that the quantum transport ofelectrons in a spin-polarized system differsgreatly from that in a spin-degenerate device.The success of dc front-gate control for themeasurement of Rashba coupling strengthinspires proposals for spin current generationby nonmagnetic means. These proposalsinclude adiabatic quantum pumping in aquantum dot with static SOI interfaced with atime-dependent barrier and a spatiallyseparated Rashba SOI region, and an ac-biasedRashba-type two-dimensional (2D) disordersystem or quantum channel. It is known thatthe translational invariance is broken in thechannel direction due to a spatially localizedtime-dependent potential, thus allowing us toexplore coherent resonant inelastic scatteringand time-modulated quasi-bound statefeatures. 11In one work, we have studied magneticopticaltransitions in a semiconductor doublering in the presence of Rashba spin-orbitcoupling and the magnetic flux. 12 First, basedon accurate numerical calculations we obtainSOI-accompanied Aharonov-Bohm energyspectra and corresponding eigenstates. Thepresence of the SOI has important influenceson the occurrence of level crossings showingResearch Activities of Individuals -›› 174

the evidence both for the periodic orbitalmotion and spin flips. We have also studiedthe temporal evolution processes in a two-leveland two three-level models. The interactionbetween external fields and the electron resultsin the successive stimulating absorption andemission of a photon and turn out as theeffective Rabi oscillators. In the two-levelmodel, we demonstrate an alternativemanipulation of electrons transiting betweentwo rings. Moreover, by short pulse excitationswe also demonstrate the possibility on optimalcontrol of selective and direct signals. Finally,we have explored the photon-assistedtunneling in the λ-type model. In addition togeneration of ROs also we give the criterion ofthe most efficient transfer via the mediatedindirect-tunnelingpaths. Further, bysuccessive pulse irradiations the well controlon pulse delay results in the time prolongationon state populations. We should alsoemphasize that in the λ-type scheme theminimization of the intermediate-levelpopulation is achieved which is an importantand practical strategy in device realization.Further, we investigate non-adiabaticallyhow the dc spin current is generated under themechanism of SOI using a dynamical allelectrical control on a split-gate-confinednarrow channel. 13 We have demonstratednontrivial features concerning the spin currentgeneration mechanism caused by differentstrength of Dresselhaus spin-orbit coupling.These results provide a robust manner ofgenerating spin current without accompanyingcharge current.The spin current generating features havebeen demonstrated and illustrated in detail. Ithas been found that the Dresselhaus spin-orbitcoupling intends to suppress the efficiency ofspin current generation in the low kineticenergy regime, while the Dresselhaus effectcan enhance the pumped spin current in thehigh kinetic energy regime. Unlike theparametric quantum pumping, in which twopumping potentials with a phase difference isneeded. Our proposed spin current generatingdevice is achievable using a single ac-biasedgate, and should be achievable within recentfabrication capability.References[1] S. Burger, F. S. Cataliotti, C. Fort, F.Minardi, and M. Inguscio, Phys. Rev. Lett.86, 4447 (2001).[2] B. Wu and Q. Niu, Phys. Rev. A 61,023402 (2000); B. Wu and Q. Niu, Phys.Rev. Lett. 89, 088901 (2002).[3] W. H. Kuan and S. C. Cheng (preprint PRA2007).[4] W. H. Kuan and S. C. Cheng (preprint PRL2007).[5] M. Ueda and A. J. Leggett, Phys. Rev. Lett.80, 1576 (1998).[6] W. H. Kuan and S. C. Cheng (preprint PRA2007).[7] J. Stuhler, A. Griesmaier, and T. Koch et.al., Phys. Rev. Lett. 95, 150406 (2005).[8] S. Yi and L. You, Phys. Rev. A 61, 041604(2000); ibid. 63, 053607 (2001).[9] Daw Wei Wang, cond-mat 07043868(2007).[10] B. Deb and L. You, Phys. Rev. A 64,022717 (2001).[11] L. Y. Wang, C. S. Tang, and C. S. Chu,Phys. Rev. B 73, 085304 (2006).[12] W. H. Kuan, C. S. Tang, and C. H. Chang,Phys. Rev. B 75, 155326 (2007).[13] C. S. Tang, W. H. Kuan, and Y. C. Chang(preprint PRB 2007).175 ‹‹- Research Activities of Individuals

Research Activities on Spin PhysicsYung-Chang Lee (Physics Department, University at Buffalo, SUNY, Amherst, NY 14260; email: phyyclee@buffalo.edu)Visiting professor, 2007/3/15~2007/7/31his must have been my 10th or 11thvisit to Taiwan, since my firstsabbatical leave which was spent at PhysicsDepartment, Tsing Hua University for twosemesters during the academic year of 1971-1972. These visits were all sponsored by thesame government agency, "The NationalCommittee of Science". They spanned over aperiod of 36 years, averaging about one visitevery three years.I have witnessed the considerablecontinuous growth of science and technology,physics in particular, over more than a third ofa century. It is, therefore, with great pleasureand satisfaction, as well as nostalgia that Iwrite this report on probably my last extendedvisit to Taiwan, now that I am ponderingretirement within two or three years.Compared to what I saw and experienced inmy last sabbatical leave also at ElectrophysicsDepartment, NCTU seven years ago, I haveseen much higher level in quality and quantityof creative output from many young facultymembers and science workers who haveworked independently and also benefited fromthe collaboration, guidance and, moreimportantly, the stimulating atmospherecreated by the more senior members of thephysics community. In particular, ProfessorsD. S. Chuu, Chon-Saar Chu in NCTU, amongmany others, had successfully guidednumerous Ph. D and M.S. students, postdoctoralfellows, young Assistant Professorswho have matured into independentresearchers. Similar achievements by othermembers in the academic community all overTaiwan are too many to be listed. It must alsobe mentioned that the participation of leadingforeign experts from Russia, Japan such asProfessor A. G. Mal'shukov etc., on short orlong term basis have provided innovativeideas, vision, and wisdom that are soinstrumental to the development andformulation of science, and physics inparticular.Overall, I am happy and excited to seescience in bloom, much more so than in thepast decades. The leadership of the variousuniversity administrations such as those ofNTHU, NCTU, NTU, NCKU and NSYSU, thefunding from government agencies and, lastbut by no means least, the improved policieswith respect to the independent focus groupsand their implementation by NCTS have allcontributed to the progress of science inTaiwan. Finally, the very successfulinternational symposiums, one on "TwodimensionalTransport involving the complexInterplay of Localization and Electron-Electron Interaction Effects", the other on"Twenty years Anniversary of Discovery ofthe High-Tc Superconductor YBCO" must becounted as the crowning events during my stayin Taiwan. I have benefited greatly from bothevents.Starting from the second week after arrival,I gave seminars at different universities,including (i) Institute of Physics, NCTU (ii)Physics Department, National TaiwanUniversity (iii) Physics Department, NCKUand (iv) Physics Department, National SunYat-sen University.Interestingly, the titles evolved over timefrom "Macroscopic Quantum Interferencewithout Cold Temperatures" to "QuantumEntanglement and Macroscopic QuantumInterference without Cold Temperatures" tothe final title "Quantum Engagement andMicroscopic Interferences en masse in aCoherently Mixed Bose Gas". This reflectedthe work being in progress as these talks weregiven. Eventually it was published as last titledin J. Phys.: Condens. Matter 19 (2007)376214. We believe it contains a totally newResearch Activities of Individuals -›› 176

concept, namely, "quantum engagement" thatis akin to but more than the familiar concept ofquantum entanglement. While the latter is apurely quantum mechanical correlation, theformer is intrinsically a quantum statisticalcorrelation for bosons not in physical spacebut rather in spin space. In the last section ofacknowledgement of this paper, "One of theauthors (YCL) would like to thank ProfessorC. S. Chu of the National Center forTheoretical Sciences, National Chiao TungUniversity (Taiwan) for hosting his visit ..."Another series of seminars on "HighTemperature Superconductivity" was startedsince the end of March, 2007, givenexclusively in Electrophysics Department,NCTU. From the very beginning of this series,it was announced that "this would be in thenature of a progress report on my own work intopics related to high Tc superconductivity. Iwould strive to give one such seminar everyweek. However, it would be interrupted if I getstuck and have nothing meaningful to reporton until further notice..." The titles of the talksranged from the Generalization of theHohenberg Theorem; the Broken symmetry;the application of the Hubbard model; thecompetition between the effects ofDimensionality on Superconductivity andAntiferromagnetism; an elementary Review ofMagnetism; the Spin in Dirac equation for atwo-band Semiconductor; and First order (v/c)Relativistic Effect (i.e., without spin-orbitcoupling) in Spintronics. The last two topicswere conceived and developed after serving onthe Master degree oral defense committee ofMr. K. Y. Chen, whose thesis "Resonantgeneration of spin dipole by a gate-inducedspin-Hall effect" was supervised by Prof. C.S.Chu. This thesis will soon be published jointlyby Chen, Chu, and Mal'shukov as an article inPhysical Review B.This series of seminars continued almostweekly (except for national holidays) until lateJune when (a) I got stuck, and (b) my wifesuccumbed to the hot and humid weathercoupled with highly polluted air in Hsinchu.She developed a health (allergy) problem sobad that the physicians strongly advised us togo back to our home base in the US as soon aswe can.To conclude this report I would be remiss ifI did not express my deepest gratitude toNCTS, and particularly to Professor Chon-Saar Chu of the focus group. Had it not beenfor his participation as well as his most ableleadership of the group, consisting of severalfaculty members and six or seven graduatestudents in various stages of research towardPh. D or M.S degree, the seminar series wouldlose all its vitality. He was the center of theselively physics activities and discussions, notonly because of his insights in almost allaspects of condensed-matter physics, but alsobecause of his innate cordiality andfriendliness. Without exception, every bodylikes him because he is so genuinely nice toevery body. You might say it stems from hisChristian faith, but I'd say it is much more.Professors J. F. Jiang, Y. J. Lin, B. L. Yang,and, of course, my dear old friend of fortyyears, Prof. Der-San Chuu who is venerated byall, provided the magic that jelled theingredients of the seminars together.177 ‹‹- Research Activities of Individuals

Research Activities on SpintronicsHsiu-Hau Lin (Department of Physics, National Tsing Hua University; email: hsiuhau@phys.nthu.edu.tw)Center scientist, 2006/2/1~2008/1/31Spintronics at Nanoscalen the past year (2006-2007), I havebeen working on various aspects ofspintronics at nanoscale. Extending ourprevious work on spin-wave theory, we tried todevelop a self-consistent Green's function(description for diluted magnetic)semiconductors [see Phys. Rev. Lett. 86, 5637(2001)]. Treating both localized and itinerantspins on equal footing, we go beyond previousstudies on thermodynamics and discoverinteresting trends of spin-wave dynamics [seeAppl. Phys. Lett. 89, 072101 (2006)]. Wepredicted that the spin-wave relaxation indiluted magnetic semiconductors woulddecrease first and eventually increase againwhen temperature increases. This iscompletely opposite to our understanding inconventional magnetic materials.With the developed spin-wave theory, westarted to investigate the non-collinearexchange coupling [see Appl. Phys. Lett. 89,2862 (2004)] mediated by itinerant carriers intrilayer magnetic junctions. For either Zeemaninteraction [Appl. Phys. Lett. 89, 032503(2006)] or Rashba interaction [Phys. Rev. B73, 241307 (R) (2006)], we calculated how theexchange coupling varies with junction width.It is rather remarkable that the trend of thenon-collinear exchange coupling depends onthe Fermi surface topology of the itinerantcarriers. For instance, a "wedding cake"topology favors the known RKKY-likeinteraction while a "donut" shape change thetrends to spiral, which is more useful for spinmanipulations at nanoscale.Meanwhile, combining both analytic andnumerical approaches, we found a novelferromagnetism in the armchair graphenenanoribbons. Our findings highlight the crucialimportance of the electron-electron interactionand its subtle interplay with the boundarytopology. The resultant magnetic ground statewith metallic conductivity is not onlysurprising from an academic viewpoint, butalso has potential applications in spintronics atnanoscale in the future.Our work attracted some attentions in theinternational community and I was invited toseveral workshops/conferences to present ourresearch results. In the following, I willdescribe the research results in details.Diluted Magnetic SemiconductorsCarrier-mediated ferromagnetism, found inResearch Activities of Individuals -›› 178

diluted magnetic semiconductors (DMS) suchas III-V semiconductors doped with transitionmetals, opens up the possibility of electricmanipulations of magnetic and opticalproperties because of the exchange couplingbetween the localized moments of thetransition metal and the itinerant spins in thesemiconducting bands. In recent years,experimental progress has stimulated intensetheoretical investigations of DMS whichmainly focus on estimates of the criticaltemperature. Although some experimental datais available little theoretical attention has beenpaid to spin dynamics, which is cruciallyimportant in understanding the spin coherence.We employ a self-consistent Green'sfunction approach to investigate the spin-waverelaxation Gamma(p) in diluted magneticsemiconductors. We find the trend of the spinwaverelaxation strongly depends on the ratioof the itinerant and impurity spin densities. Fordensity ratios in the so-called Ruderman-Kittel-Kasuya-Yosida phase, Gamma(p)decreases even though thermal fluctuationsincrease. On the other hand, in the strongcoupling phase, an interesting peak structureappears.To analyze how spin waves relax in DMS,both the itinerant and impurity spins need to betreated on an equal footing. We employ theself-consistent Green's function approach thatretains both spatial and thermal fluctuations, toinvestigate the spin-wave relaxation at finitetemperatures. The Green's functions allow usto numerically compute the spin spectralfunction and therefore the spin-waverelaxation. One may naively expect a smoothincrease in the spin-wave relaxation as thermalfluctuations grow. However, our numericalresults go against common intuition. Forinstance, in the RKKY phase, the spinrelaxation actually decreases with increasingtemperatures.The magnetization curve and the spinrelaxation rate are closely related. In addition,they also sensitively depend on the densityratio n_h/n_I. This is reminiscent of theinteresting differences between as-grownsamples and annealed ones. The annealingprocess removes interstitial impurities andreduces the disorder strength. However, if theas-grown sample is already in the diffusiveregime, the annealed one can also be describedby the virtual crystal approximation. Webelieve the major difference arises from theincrease in carrier density and thus the densityratio n_h/n_I. The annealing process increasesn_h/n_I from the strong coupling to the RKKYphase which changes the shape of themagnetization curve. Therefore, it would beexciting to study the spin dynamics for bothas-grown and annealed samples and comparethe experimental outcomes with our numericalpredictions. Note that we did not include therealistic six-band Luttinger model here. Inprinciple, our approach can be generalized toinclude more bands by introducing moreGreen's functions but the self-consistentequations will be rather complicated, not fatalthough. However, it is important to emphasizethat the ratio n_h/n_I to enter the RKKYregime is expected to be larger, as compared tothe estimate from the two-band model.Carrier-Mediated Non-collinearExchange CouplingThe central theme of spintronics is tomanipulate the extra spin degrees of freedomin condensed matter systems as compared withthe traditional electronic devices where onlythe charge part was utilized. One of the classicexamples, which merges charge and spinsectors together in a single device is the spinfield effect transistor (SFET) proposed byDatta and Das more than a decade ago. It wassuggested that the Rashba interaction, whosestrength is controlled by the gate voltage,causes the spins of the itinerant carriers tospiral and can be used to modulate the179 ‹‹- Research Activities of Individuals

transport currents. Another more recentproposal, now under the name of spin Halleffect, explores the possibility to generate spincurrents (or spin accumulations) by electricgates via spin-orbital interactions and hasreceived some primitive verification inexperiments.On the other hand, it is less explored howthe spin-orbital interaction will reshape ourunderstanding in the more conventionalmagnetic junctions. We study the non-collinearexchange coupling across the F/N/F trilayermagnetic junction (TMJ), where theintermediate layer consists of semiconductors(such as GaAs) with significant Rashbainteraction. Since the TMJ resembles theDatta-Das SFET, one may naively guess thatthe carrier-mediated exchange coupling can beexplained following similar arguments. Withinthe single-particle picture, Datta and Das haddemonstrated the spins of the itinerant carriersundergo precessions due to the Rashbainteraction and, therefore, lead to the noncollinearcoupling between the ferromagneticlayers.However, there is a sharp differencebetween SFET and TMJ. In the SFET, thetime-reversal symmetry is broken (by thesource-drain bais which drives the current)while, in the TMJ, the symmetry is preservedand gives rise to Kramers degeneracy. In fact,this non-trivial degeneracy has a profoundinfluence upon the effective exchangecoupling across the junction. It turns out thatthe single-particle picture (with specificmomentum) employed in Datta-Das' originalwork fails to explain the magnetic behaviorbecause the inclusion of the whole Fermisurface is crucially important. For instance, thequantum interferences between the Kramersdegeneratepatches of the Fermi surfaces giverise to the oscillatory RKKY interaction. Toexplore the subtle competition between thespiral and the RKKY interactions, one needs tointegrate over the whole Fermi surfaces bynumerical approach.The outcome is rather surprising -- thedominance of either spiral or RKKYinteractions depends on the topology of theFermi surface. When the Rashba interaction isweak (compared with the Fermi energy), theFermi surface consists of two cocenteredcircles with opposite chiralities. In this regime,the RKKY interaction dominates over thespiral. However, as one gradually increases thestrength of the Rashba interaction, the innerFermi circle shrinks to zero first, reappearsagain but with the same chirality as the outercircle. The topological change of the Fermisurface magically alters the dominant couplingfrom the RKKY to the spiral. Therefore, in thestrong Rashba limit, the non-collinearexchange coupling mainly comes from thespiral interaction with minor quantumcorrections. It is rather amazing that thetransition between different magneticbehaviors coincides with the change of theFermi surface topology.Magnetism in Armchair GrapheneNanoribbonOne of graphene's superior properties is itspronounced ambipolar electric field effect. Byapplying gate voltages, the charge carriers canbe tuned between electrons and holes withconcentration up to 1013 cm-2. Making use ofthe sensitivity to the electric field, Son, Cohenand Louie demonstrated zigzag graphenenanoribbons (GNR) can become half metallicand their magnetic properties can be controlledby the external electric field. Their results notonly show that the electronic spin degrees offreedom can be manipulated by the electricfields, but also bring up the possibility toexplore spintronics at the nanometer scalebased on graphene.Since open boundaries of GNR play acrucial role at nanoscale, we expect theinterplay between Coulomb interaction and theedge morphology will lead to rich physics. It isResearch Activities of Individuals -›› 180

then interesting to study GNR with armchairedges. Note that the edges are hydrogenated sothat the dangling sigma bonds are saturatedand only the pi bands remain active in lowenergy. By combining analytic weak-couplinganalysis, numerical density matrixrenormalization-group (DMRG) method, andthe first-principles calculations, we show thatarmchair GNR exhibits novel carrier-mediatedferromagnetism upon appropriate doping.Even though only pi bands are active inlow-energy, in appropriate doping regimes, thearmchair edges give rise to both itinerantBloch and localized Wannier orbitals. As willbe explained later, these localized orbitals aredirect consequences of quantum interferencesin armchair GNR and form flat bands withzero velocity. The carrier-mediatedferromagnetism can thus be understood in twosteps: Electronic correlations in the flat bandgenerate intrinsic magnetic moments first, thenthe itinerant Bloch electrons mediateferromagnetic exchange coupling among them.As a result, the magnetic properties ofarmchair GNR sensitively depend on thedoping and thus can be manipulated by theexternal electric fields.Besides its potential applications tospintronics at nanoscale, the ferromagneticground state in the armchair GNR also revealsa new type of flat-band ferromagnetism,different from those proposed by Mielke andTasaki. The key to Mielke-Tasakiferromagnetism is the finite overlap ofadjacent Wannier orbitals in the flat band.Once the so-called local connectivity conditionis achieved, the finite overlaps generateexchange coupling among these orbitals,leading to flat-band ferromagnetism. However,the Wannier orbital in armchair GNR has zerooverlap with its adjacent neighbors. The flatband alone only accounts for the existence ofthe magnetic moments and the ferromagneticorder sets in only when itinerant carriers arepresent.181 ‹‹- Research Activities of Individuals

Research Activities on Spin PhysicsKao-Chin Lin (email: kclin@phys.cts.nthu.edu.tw)Postdoctoral researcher, 2006/12/1~presenty last research topics before I wasoffered the postdoctorship from theNCTS is the electron-photon interactionassociated with the uncertainty basedtunneling (EPAUT). During the earlier periodas the postdoctor in NCTS, my main project isto continue my previous research. The interdotCoulomb interaction and the Kondo effect areconsidered.I considered the electron interacting withthe detuning photon field quantummechanically in a parallel coupling doublequantum dot(DQD) system. In the DQDsystem, each QD is coupled to the lead andbecomes a subsystem. I employed the detuningphoton field to open an energy-timeuncertainty for electron tunneling between QDand lead. The process in which electrontunnels between the QD and the lead via theenergy-time uncertainty is called electronphotonassociated uncertainty based tunneling(EPAUT) in my research.Some new results are pointed out asfollows.(1) Unlike the Kondo effect in which theCoulomb interaction is the necessarycondition and is a two particle problem, theEPAUT is arised even the situation inwhich one electron is considered or theCoulomb interaction is ignored. I Shouldemphasized that the EPAUT is not equal tothe Kondo effect. This factor is reflected onthe EPATU corresponding self-energy inwhich the Kondo effect interacting quasiparticleis scattered by the EPAUT and inthe form of the direct product of theEPAUT coupling energy and Greenfunction of Kondo effect.(2) The characteristic temperature iscalculated. There are three regions oftemperature. When the detuning factor islarger than the characteristic temperature,the characteristic temperature decreasesexponentially with the incensement ofdetuning factor. When the detuning factoris in order of or smaller than thecharacteristic temperature, the EPAUT isdominated by the thermal effect and thecharacteristic temperature is insensible ofthe detuning factor.(3) Besides the detuning factor, the EPAUTeffective electron-photon coupling strengthis tunable via tuning the Fermi energy ofthe lead. The strength of the EPAUT andelectronic current via the EPAUT channelare maximum when the energy differencebetween the energy levels of QDs and theenergy differencebetween the Fermenergy of thesubsystems areequal.These results havebeen submitted to PRBand Journal of physics :Condensation matter.Research Activities of Individuals -›› 182

Research Activities on Accelerated Detector - Quantum FieldSystemShih-Yuin Lin (email: sylin@phys.cts.nthu.edu.tw)Assistant research scholar, 2006/8/1~presenty research is mainly on theories ofquantum particles or atoms coupledwith quantum fields. I have been working onthis topic in collaboration with Prof. Bei-LokHu at University of Maryland since 2004. Weare looking at the properties of the vacuum,the response of the accelerated particle to thevacuum, the radiation emitted by theaccelerated particle, and the radiation reactionto the particle in curved space.We had worked out a complete, exactevolution of the Unruh-DeWitt detector theoryin (3+1) dimensional Minkowski space [1],which can be related to quantum Brownianmotion of harmonic oscillators. The radiationemitted by the detector and observed at thenull infinity of Minkowski space has beenobtained from initial transient to final steadystate.Applying the non-perturbative results weobtained in Heisenberg picture, we expressedthe reduced density matrix in terms of twopointfunctions to study the quantum statisticalproperty of the detector. We discovered newfeatures in the dynamical evolution of thedetector's internal degree of freedom, andidentified the Unruh effect derived originallyfrom time-dependent perturbation theory asoperative in the ultra-weak coupling and ultrahighacceleration limits [2,3]. The mutualinteraction between the detector and the fieldengenders entanglement between them, andtracing out the field leads to a mixed state ofthe detector even for a detector at rest inMinkowski vacuum. Different from thoseconventional results in which the quantumfield's back-reaction is ignored, our findingsbased on the exact solution shows clearly thatthe detector no longer behaves like a perfectthermometer. From a calculation of theevolution of the reduced density matrix of thedetector, we find that the transition probabilityfrom the initial ground state over an infinitelylong duration of interaction derived from timedependentperturbation theory is existent in theexact solution only in transient under speciallimiting conditions corresponding to theMarkovian regime. Furthermore, the detectorat late times never sees an exact Boltzmanndistribution over the energy eigen-states of thefree detector, thus in the non-Markovianregime covering a wider range of parametersthe Unruh temperature cannot be identifiedinside the detector.While we have broadened the research onthe Unruh effect to the realm of nonequilibriumstatistical physics, we arecurrently focusing on the modern quantuminformation issues in the Unruh-DeWittdetector theory. Using our non-perturbativeresults we are able to look at the quantumdecoherence and recoherence processes in asingle detector as well as the quantumentanglement between two accelerateddetectors over the whole parameter range. Weexpect that our results can help to answer thequestions of the entropy and informationraised in black hole physics and quantumgravity.References[1] S.-Y. Lin and B. L. Hu, Phys. Rev. D 73,124018 (2006) [gr-qc/0507054].[2] S.-Y. Lin and B.L. Hu, Found.Phys. 37, 480(2007) [grqc/0610024].[3] S.-Y. Lin and B.L. Hu, Phys. Rev.D 76, 064008 [grqc/0611062].183 ‹‹- Research Activities of Individuals

Research Activities on Spin Transport in SemiconductorsAnatoly G. Mal'shukov (Institute of Spectroscopy, Russian Academy of Sciences and Department of Electrophysics,National Chiao Tung University; email: malsh@isan.troitsk.ru)Center scientist, 2007/1/1~2008/6/30n 2007 my research activity in NCTShas been focused on spin transport insemiconductors. Most of the work was on thespin-Hall effect (SHE) and related phenomena.A conventional set up for studying this effectis a 2D quantum well with an electric fieldapplied parallel to the heterointerface. Thisfield drives a spin current in the directionperpendicular to it. Spins in such a current areoriented along the normal to the quantum well.Since the spin current consists of two counterfluxes of oppositely directed spinpolarizations, the total polarization in thenormal direction is zero. At the same time, thespin polarization of 2DEG in the paralleldirection is not zero due to the so calledelectric spin orientation effect which is closelyrelated to SHE. Together with Prof. C. S. Chufrom NCTU we considered [1] SHE and theelectric spin orientation in a set up quitedifferent from the conventional one. Instead ofthe planar electric current, which drives SHEand spin orientation, we considered atunneling current perpendicular to the quantumwell. A rectangular double barrier system wastaken as a model. An important distinctionfrom the traditional approach is that one cannot consider such a problem using a spin-orbitinteraction (SOI) averaged over quantum wellconfinement. To make this distinction moreclear we considered a symmetric quantum wellwhere Rashba SOI is absent after averagingover confinement. In such a situation oneshould consider the initial SOI associated withgradients of material parameters across theQW heterointerface. It has been shown thatthis SOI, together with the bulk Dresselhausinteraction, give rise to the electric spinorientation with polarization directedperpendicular to the quantum well. The currentof spin polarization directed parallel to thequantum well has been also predicted. A veryconvenient way to observe these effects isSTM with a magnetic tip. With somemodification our results can be applied tometal surfaces carrying surface states with alarge spin orbit splitting.As known, the spin-Hall effect leads toaccumulation of the spin polarization near thesample boundaries. The spin density can bealso accumulated near impurities. Weconsidered [2] the nonequilibrium spin densityaround a potential barrier having the form of amesoscopic 2D ring. The spin orbit interactioncaused by gradients of the potential is stronglyenhanced due to semiconductor band structure.We found that the accumulated spinpolarization has the form of a dipole.Moreover, the strength and the sign of a dipolestrongly depend on the position of the Fermilevel with respect to transmission resonancesof the ring structure. Besides this specialgeometry, we are considering [3] a traditionalproblem of spin accumulation near boundariesof a 2D strip with Rashba and Dresselhausinteractions plus a magnetic field parallel tothe quantum well. We found that there is nospin accumulation when only Rashbainteraction takes place, independent on thepresence or absence of the magnetic field.The spin relaxation rate is an importantparameter for various spintronic applications.In semiconductors at low temperatures themajor mechanism of spin relaxation is the socalled D'yakonov- Perel' relaxation due to theSOI effect. It has been shown several yearsago that this mechanism is strongly suppressedin systems with restricted geometry. Forexample, a dramatic slowdown of the spinrelaxation has been predicted for quantumResearch Activities of Individuals -›› 184

wires. Indeed, such a slowdown has beenrecently observed in quantum wires. Theobserved behavior, however, does not agreewell with theoretical predictions, based on thediffusion approach to spin transport. Togetherwith Prof. C. H. Chang [4] we tried tounderstand such a discrepancy using a methodof classical trajectories. This method can beapplied for calculation of the spin relaxationtime within a broad range of parameters,including a ballistic case. Now this work is inprogress.Resonant spin dipole induced by an inplanepotential gradient in metallicconduction, Phys. Rev. B, accepted[3] L.Y. Wang, C.S. Chu, A.G. Mal'shukov, inpreparation[4] C.H. Chang, A.G. Mal'shukov,Semiclassical path integral approach tospin relaxation in quasi-1D wires, inpreparationReferences[1] A.G. Mal'shukov, C.S. Chu, Spinorientation and Spin-Hall effect induced bytunneling electrons, submitted to Phys.Rev. B[2] K.Y. Chen, C.S. Chu, A.G. Mal'shukov,185 ‹‹- Research Activities of Individuals

Research Activities on Condensed Matter PhysicsBaruch Rosenstein (Department of Electrophysics; email: baruchro@hotmail.com)Center scientist, 2007/1/1~2007/12/31uring last several years there is a cleartrend in experimental physics toadvance towards construction of facilitiesproviding magnetic fields in the 100 Teslarange. Existing facilities include the NHMFL,Tallahassee (45T DC), Los Alamos 60 (100 mspulse) and just completed Dresden 100T(10ms). These facilities are profoundlydifferent from those appearing ten years ago inJapan and elsewhere which could provide onlya very short pulse in this range. The newfacilities operate in the DC mode or in thefrequency range suitable for condensed matterresearch. Taiwan is also currently consideringbuilding such a facility. The 50-100T rangeopens a lot of new possibilities for condensedmatter physics (as well as for certain materialscience, biological sciences experiments).Examples of already existing areas are:Quantum Hall effect (fractional QHE andnewer discoveries can be observed only above30T), deHaas-van Alfven effect in metals andsuperconductors, vortex matter in high Tcsuperconductors (which have Hc2 above100T), dephasing in disordered metals andsemiconductors, magnetism (phase diagram ofmanganites extends well into 50T range) andspin physics. Physically the 100T rangecorresponds to magnetic length in thenanometer range and energy range of 0.1 eV.European Union have already organizedInternational conference on TheoreticalPhysics in High magnetic fields (CorrelatedElectrons in HMF, Ein Gedi, Israel, December2004 and Recent Trends in Theory of PhysicalPhenomena in High Magnetic Fields II,Dresden, Germany, October 2006) . The fielddefinitely requires theoretical support. Firsttextbook on the physics in high magneticfields have already appeared (Vagner et al,Springer)My mission was1. To initiate and promote a cutting edgeresearch in the area of condensed matterphysics in strong magnetic fields. Thisoverlaps with activities of both theCorrelated Electron Systems andMesoscopic Physics focus group. For thisseveral leading physicists should be invitedas visitors.2. Organize International workshop on thetopic.3. Organize education of graduate student bygiving a course on physics in magneticfields. The field is highly specialized andseparate from other topics (for example,notoriously dominated by the Landau levelsconcept, less dissipation, spin's importance).Accomplished goals1. I started the research in this field and willcontinue it next half a year. Includes bothanalytical methods (with help of NCTSvisitors V. Zhuravlev (Max Planck,Dresden) and D.P. Li (Beijing U) andnumerical.2. Have given a course for both NTHU andNCTU graduate students on the topic.3. Have given a 3 hour lecture at NCTS as partof the "Introduction" course.4. Started to organize a program and aworkshop in collaboration with ArgonneNational lab. It includes inviting severalleading experts in the field including Dr.Vinokur (Argonne) and A. Gurevich(Magnetic lab.,Tallahassee). Willuse the designatedm o n e y(200.000$NT) toinvite speakers tothe workshop thatis planned forDecember 2007.Research Activities of Individuals -›› 186

Research Activities on Quantum Control of QubitsKazuomu Shiokawa (email: kshiok@phys.cts.nthu.edu.tw)Visiting scientist, 2006/4/4~presentuantum information science andtechnology is currently one of themost active fields of research in science. It isalso an interdisciplinary field that overlapswith many different areas in theoretical andexperimental sciences including computerscience, mathematics, engineers, chemistry,physics, etc. Thus it provides a good topic tobe pursued at the institute such as NCTSwhich has interdisciplinary themes andresources.In quantum computation, its capability ofproviding the solution for certain problemsfaster than classical computer has importantpractical applications such as communicationsand cryptography. However, actualimplementation of quantum informationprocessors requires the precise manipulation ofsmall quantum systems with high precision.The most serious obstacle against therealization of quantum processors is theinteraction with its surrounding environmentwhich destroys quantum coherence, theessential resource of fast computation. Thisphysical process is called decoherence.Therefore, it is crucial to understand theprecise mechanism of decoherence and inventbetter and realistic methods to preventquantum processors from decoherence.Most naïve theories of quantum computingassume a coupled-spin system. This naïvemodel fails to explain the realistic phenomenain many ways when it comes to the specificimplementation. In a recent few years, I havebeen developing systematic methods to studyquantum computation in a generalenvironment. In my previous works [1] and[2], some exact solutions for generalized spinboson models are found and analyzed.The spin-boson model is a standard modelfor qubits in a general open quantumenvironment. Reduced dynamics of this modelfollows nonlinear evolution and is difficult toanalyze. Most common approaches are toinvoke Born-Markov type approximation.However, at low temperature and strongsystem-bath interactions where manyexperiments in quantum information areperformed, this approximation is no longervalid. Other common methods such as weakcoupling approximations do not guarantee thepositivity of quantum state evolution and maynot be reliable for the precise analysis ofquantum properties sensitive to this issue suchas quantum entanglement. Therefore the exactsolutions are extremely useful for thefundamental understanding of the nature ofquantum computing at low temperature.Fig. 1 The decay rate of population at T=0 in (a) and atT=20 mK in (b). The solid curve is our exact result,while the dashed lines are from using the Born-Markov Apporoximation Ω=1 GHz, γ=0.2 GHz, andΛ=100 GHz.187 ‹‹- Research Activities of Individuals

In Figure 1, the exact evolution of thedecay rate is plotted and compared with theBorn-Markov result for zero and finitetemperature. The decay rate under exactevolution is strongly time-dependent while it isjust a constant under Born-Markovapproximation.With the close solutions for generalizedspin boson models, it is possible to explore theexternal pulse control of quantum bits in moredetail than previously done by other methodsunder various approximations [5].In order to protect quantum devices fromenvironment-induced decoherence, variousquantum error correcting codes are invented[3]. Dynamical decoupling is an active way ofprotecting qubits by using a fast control pulseto cancel the net effect of environment beforeit leads to destroy the coherent evolution of thesystem. It was shown to be extremely effectiveto eliminate the 1/f noise which is a commonsource of decoherence of qubits where thecontrol is provided by electronic devices [4].Fig. 2 (a) Coberence as a function of pulse interval at T=0is plotted. t=0.25(ns). Parameter are:Λ UV =100(GHz), Λ IR =1, γ=0.125(GHz) for Ohmic, andγ=0.005(GHz) for super-Ohmic case. (b) Plots of thefirst excited state population at T=0 and t=0.15(ns).Other parameter values are: Λ UV =100(GHz),Ω=1(GHz), γ=0.1(GHz) for Ohmic, andΛ UV =100(GHz), Ω=1(GHz), γ=0.5(GHz) for 1/ƒ,Λ UV =50(GHz), Ω=10(GHz), γ=0.01(GHz) for super-Ohmic case. Parameter values are chosen to fit allthe curves in the parameter range in the figure, Forthe same parameter values, while their qulitativebehavior remains similar, the differences in theirvalues are more striking.In Figure 2, the effects of dynamicaldecoupling pulses are shown. The puredephasing model (a) and exact generalizedspin-boson model both show the performancemore effective on decoupling 1/f noise andless effective on super Ohmic noise. Importantdifference is that the former (in (a)) shows thecomplete elimination of coherence at theresonant pulse frequency, who appears to bedisastrous. However, this is not observed inlaboratory experiments. Our exact solution (in(b)) does not show such behavior and correctlyagrees with experiments.References[1] K. Shiokawa and R. Kapral, J. Chem. Phys.117, 7852 (2002).[2] K. Shiokawa and B. L. Hu, Phys. Rev. A70, 062106 (2004).[3] M. A. Nielsen and I. L. Chuang, QuantumComputation and Quantum Information,Cambridge University Press, Cambridge,(2000).[4] K. Shiokawa andD. A. Lidar, Phys.Rev. A 69, 030302(2004).[5] K. Shiokawa andB. L. Hu, QuantumInformationProcessing, V. 6,55 (2007).Research Activities of Individuals -›› 188

Research Activities on String TheoryYi Yang (email: yyang@phys.cts.nthu.edu.twAssistant Research Scholar, 2006/8/1 – presenty research interesting is on stringtheory, and string related theories.During the last year, I have been workingmainly on the study of the relationshipbetween the high energy behavior of stringscattering amplitudes and the hiddensymmetry in string theory. As it is well known,the most important property of string theory isthat string theory is a finite theory, i.e. stringtheory does not need renormalization to get aphysical result. This wonderful property isbecause of the milder high energy behavior ofstring scattering amplitudes comparing to theconventional quantum field theory (QFT). InQFT, the high energy behavior of scatteringamplitudes follows a power law. On the otherhand, the high energy behavior of stringscattering amplitudes enjoys an exponentiallaw, which decreases much faster than thepower law. This faster decrease in ultra-violet(UV) leads to the finite results in string theory.However, in string theory, there are infinitymassive modes in UV comparing to the finitemodes in QFT. Instinctively, people will thinkthat in the high energy limit, there will bemore and more scattering channels contributeto the amplitudes in string theory and make itmore divergent than in QFT. Therefore, theremust be a hidden symmetry in string theory toinduce a cancellation among the infinitychannels. This symmetry should be infinitylarge. Study this hidden symmetry directly isdifficult, we therefore turn to study the highenergy scattering amplitudes for the fixedmass levels. In our previous work, we haveproved that for any fixed mass level in stringtheory, the different amplitudes are linearrelated each other although they have differenttensor structures. It is then natural toconjecture that these linear relationscorrespond to the hidden symmetry in stringtheory. We continued our study in thisinteresting subject and extended it to the casesof closed string and superstring. The similarlinear relations were found. In the last year, wefurther extended our study to the case ofincluding D-brane. D-brane is a nonperturbativesoliton-like object in stringtheory; its existence extraordinarily enrichesthe string backgrounds. We systematicallystudied closed strings scattering from a rigid(i.e. no back reaction) D-brane in [1, 2, 3], wefound that, for most of the D-branes, there aresimilar linear relations among the high energystring scattering amplitudes. While for adomain-wall brane, i.e. a (d-2) dimension D-brane in d dimensional space-time, the linearrelations break down. We then found that,when the linear relations breaking down, theexponential-law behavior reduces to a powerlawbehavior at the same time. This is a perfectanti-example to validate our conjecture that thesymmetry (linear relations) corresponds to thehigh energy behavior of string scatteringamplitudes. To clear our point, we recentlystudied winding closed strings scattering in acompact space-time in [4]. Another antiexamplewas found in this case, i.e. when wemove from Gross regime to Mande regime,some of linear relations break down, and thecorresponding high energy scatteringamplitudes will be reduced from exponentiallawto a power-law.Recently, I am interesting in studying the socalled AdS/QCD duality. This is a realisticversion of the original AdS/CFT duality instring theory. In AdS/CFT duality, the type IIBstring theory in an Anti-de-Sitter (AdS) spacetimeis conjectured to dual to an N=4supersymmetry Yang-Mills field theory, whichis a conformal theory (CFT) on the boundaryof AdS space-time. Compatifying a spacedimension on a circle to break allsupersymmetries, and adding flavor D-branes,189 ‹‹- Research Activities of Individuals

the boundary field theory is conjectured todual to QCD. Of many AdS/QCD models,Sakai-Sugimoto model is the most promisingone and has been studied extensively duringthe last several months. Some meson spectrumwas calculated by AdS/QCD and the resultshave been compared to the experimental dataand to lattice QCD, a good agreement wasobtained. In addition, spontaneously chiralsymmetry breaking has been constructed in themodel and Goldstone boson is identified withpion, whose action is consistent with Skyrmemodel. The AdS/QCD at finite temperaturehas also been studied. Confinementdisconfinement,χS/χSB phase transitionswere studied; the results are consistent withthe ones obtained by lattice QCD. However,there are still many questions remained in themodel. Now I am collaborating with the NCTSmembers in phenomenology focus group. Weare going to systematically study theAdS/QCD for different string backgrounds andthe corresponding "QCD" theories. Hopefullywe can effectively fixed the parameters and tomake some predictions for the coming LHC.During the last year, I have attended twoconferences. One is in Vietnam where I givena talk about my work in NCTS. The other isthe annual conference of Strings2007 in Spain.I would like to thank NCTS to support meattending the international activities.References[1] C.T. Chan, J.C. Lee and YY, Scatterings ofMassive String States from D-brane andTheir Linear Relations at High Energies,hep-th/0610062, Nucl.Phys. B764 (2007)1-14.[2] C. Chan, J.C. Lee, Y.Y., "Power-lawBehavior of Strings Scattered fromDomain-wall and Breakdown of TheirHigh Energy Linear Relations", hepth/0610219.[3] J.C. Lee, Y.Y., "Linear Relations ofAbsorption/Emission Amplitudes of D-brane", hep-th/0612059, Phys.Lett. B646(2007) 120-124.[4] J.C. Lee, Y.Y., "Linear Relations and theirBreakdown in High Energy Massive StringScatterings in Compact Spaces",arXiv:0705.1872, (Accepted by Nucl.Phys.B).Research Activities of Individuals -›› 190

Research Activities on Computational Materials ResearchZizhong Zhu (Department of Physics, Xiamen University; email: zzhu@xmu.edu.cn)Visiting professor, 2007/3/8~2007/9/8started my visit of Taiwan on March8, 2007, and returned home onSeptember 7, 2007. The duration of my visit issix months. Under the support of NationalCenter for Theoretical Sciences (NCTS), I hadthe honor to have visited several universitiesand institutions in Taiwan and discussed withmany scientists who are experts in the field ofcomputational material sciences. I benefit a lotby these discussions and have also createdmany opportunities for future cooperation.Here, I present a brief report on my experienceand achievement of this visiting.On the aspect of academic interactions:(1) I gave a talk of "First-principles, MolecularDynamics and EAM potentials: recentworks in our CMP group" at the PhysicsDepartment of National Taiwan Universityon March 22, 2007, and have discussedwith Prof. G. Y. Guo and his groupmembers as well as the graduate students.(2) On April 10, 2007, I presented a talk"Computer Simulations on someNanostructures: classical MD and Ab initiomethods" at the Institute of Physics,Academia Sinica, and discussed with Prof.Horng-Tay Jeng and other scientists fromthe nanomaterials research group.(3) May 21-22, 2007, I visited National ChungCheng University, and gave a talk on the"Ab initio method and Classical MDSimulations on Nanostructures". I havealso discussed with Prof. T. C. Lueng aswell as the graduate students.(4) On May 28, 2007, I visited National SunYat-Sen University, and discussed withProf. Feng-Chuan Chuang on thecomputational material physics.(5) On August 23, 2007, I presented a talk atthe group of Prof. G. Y. Guo of NationalTaiwan University. The title is "Magnetismof Nanostructured s- and sp-electronElements: Ab initio calculations", which isbasically a summary report of my researchcooperation with Prof. Guo during thisvisit.Except for many communications withmaterial scientists in Taiwan, I have alsoattended several mini-schools supported by theNCTS. I have gained many new ideas andlearned a lot of advanced information ofmodern material physics, which will be ofgreat importance in my future studies. Themini-schools are:(1) March 2007, the "Mini-school on timedependentDensity Functional Theory", hold atNational Taiwan University; (2) May 25-26,2007, the "Mini-School on Tight BindingSimulation of Nanomaterials", hold atNational Cheng Kung University; (3) August27-28, 2007, the "Mini-School on Fast O(N)Electronic Structure Calculations: Principlesand Implementation in the OpenMX package",hold at National Taiwan University.On the aspect of scientific research:I have cooperated closely with Prof. G. Y.Guo of National Taiwan University, andcarried through the studies on the "Magnetismof Nanostructured s- and sp-electronElements". The possibilities of elements withonly s- or sp-valence electrons to exhibitmagnetism under nano-scale structures havebeen explored. We have shown that thesesystems can show magnetism under eitherbond elongation or bond compression at onedimensionalchain structures. The paper is nowin preparation. We have also calculated theelectronic and structural properties ofLi 2 MSiO 4 (M = Mn,Fe, Co, Ni) for themodern lithium-ionbatteries. The paperhas been underrevision.Thank you verymuch for giving methe opportunity to visitTaiwan.191 ‹‹- Research Activities of Individuals

Introducing New MembersProf. Chung-Hsien ChouCenter scientist (Ph.D., National Tsing Hua University)email: chouch@mail.ncku.edu.twefore joining the National Center forTheoretical Sciences, I was apostdoctoral researcher at Institute of Physics,Academia Sinica from where I started myresearch career after graduating from theNational Tsing-Hua University under thesupervision of late Prof. Darwin Chang.During my stay at Academia Sinica, Ibenefited from the active and stimulativeatmosphere and gradually enlarged my scopeof research. Not only particle physicsphenomenology, astroparticle physics,quantum theory of gravity, and quantuminformation science are all on my list.My research interests can be broadlycharacterized in two categories:(1) High energy physics: We need to gobeyond Standard Model physics, but how?What s the nature and properties of darkenergy and dark matter? What s theorigin and nature of the ultra high energycosmic rays? How to consistently combinequantum mechanics and general relativity?(2) Quantum information science: With aparticle physicist background, my interestin quantum information science focus onthe application of field theory techniques toexamine fundamental issues in quantummechanics such as quantum decoherence,quantum entanglement, quantumteleportation, etc.Dr. Kazuyuki FuruuchiStaff scientist (Ph.D., Osaka University)e-mail: furuuchi @phys.cts.nthu.edu.twresearch interest is on deeperunderstanding of the laws that governelementary particles and the universe. In thepast I have worked on instantons on oncommutativespace, string field theory, matrixmodels and black hole thermodynamics viaAdS-CFT correspondence.Introducing New Members -›› 192

Dr. Takayuki HirayamaPostdoctoral researcher (Ph.D., Kyoto University)email: hirayama@phys.cts.nthu.edu.twam a NCTS postdoc starting fromSeptember 2007. My interest intheoretical physics is wide including QCD,extra dimensions, SUSY and SUSY breaking,black holes, AdS/CFT, D-branes and stringtheory. I have been approaching the physicsbeyond SM through field theoretical analysis.Meanwhile I have been applying AdS/CFT foranalysing strongly coupled gauge theories andfor modeling new physics at TeV scale likeHiggsless models.I like to discuss various topics, model buildingand phenomenology, field theory, more stringystuffs and so on.Prof. C.-J. David LinStaff scientist (Ph.D., University of Edinburgh)email: dlin@mail.nctu.edu.twy research hightlight last yearincludes:1). The investigation of matrix elements ofneutral B mixing using Heavy MesonChiral Perturbation Theory: With WilliamDetmold, we studied the chiral behaviourof these mtrix elements and discovered thatthe light-quark mass dependence of thematrix elements for B mixing beyond theStandard Model would be morecomplicated than that of the StandardModel matrix element. We identified theorigin of this complication to be the effectof heavy quark spin symmetry breaking inthe operators. We also used these results toinvestigate finite-volume effects in thesematrix elements, and found that they wouldbe a few percent on currently availablelattices. Finite-volume effect in one of thematrix elements is plotted as a function ofthe pion mass in the figure.2). Numerical calculations in lattice gaugetheory: Since I moved back to Taiwan inFebruary, I have been setting up facilitiesfor numerical calculations in lattice gaugetheory. These include the purchase of a PCcluster dedicated to such research avenueand the tests of softwares (QMP, QDP andCHROMA) on such a cluster. In the future,I will use these facilities to investigate therole played by strongly-coupled gaugetheories in LHC physics. In addition toQCD matrix elements for the LHCbprogramme, I am also working on topicssuch as Walking Technicolour and theBanks-Zaks infrared fixed point.193 ‹‹- Introducing New Members

Dr. Yu-Pin LuoPostdoctoral researcher (Ph.D., Chung-Yuan Christian University)email: ypluo@phys.cts.nthu.edu.twn 2005, I got Ph. D. degree in Chung-Yuan Christian University. During thepost-graduate study for my Ph.D. degree, Imainly worked on two directions, one is theprotein folding problem and the other is theIsing model on two-dimensional lattices withperiodic/aperiodic boundary conditions. Thenafter military service for one year, now I ampostdoctoral research associate in NCTS.Dr. Tzu Chiang YuanAssistant research fellow (Ph.D., Northeastern University)email: tcyuan@phys.cts.nthu.edu.twearned my PhD at 1986 fromNortheastern University under theguidance of professor Pran Nath. My thesiswork was about low energy phenomenology ofminimal supergravity model, including muonanomalous magnetic moment, proton decayand production of gaugino pair from electronpositronannihilation.During my various postdoc career atVanderbilt University, NorthwesternUniversity and University of California atDavis, I had explored other areas of particlephysics and had made important contributions.These includes topics in phase transition atearly universe, CP violation, quarkoniumphysics, QCD corrections to Higgs processes,hot QED, etc.In the past two years since I came toNTHU, I had been collaborated with variousphysicists in different institutions and workedon various phenomenology topics includingglueball, little Higgs, hidden milli-chargedfermion in Stueckelberg Z' model as darkmatter, etc. My most recent work is aboutunparticle physics. My research interest ismainly in the area of phenomenology beyondthe standard model and its implications incollider physics as well as astrophysics.Introducing New Members -›› 194

101, Section 2, Kuang Fu Road, Hsinchu, Taiwan 30013Mathematics DivisionTel: 886-3-5728263Fax: 886-3-5728161e-mail: math@math.cts.nthu.edu.twhttp://math.cts.nthu.edu.tw/Mathematics/index.htmlPhysics DivisionTel: 886-3-5734969Fax: 886-3-5735086e-mail: cts@phys.cts.nthu.edu.twhttp://phys.cts.nthu.edu.twOctober 2007