Annual Report 2008 - Fields Institute - University of Toronto

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Thematic Programs Speakers: (in alphabetical order) Florin Boca (UIUC) Continued fractions and operator algebras Bruce Blackadar (Nevada at Reno) (Title not available) Etienne Blanchard (Institut de Math de Jussieu) Proper infiniteness and K 1 injectivity (joint work with R. Rohde and M. Rordam) Nate Brown (Penn State) Metric space associated with tracial C*-algebras Marius Dadarlat (Purdue) The homotopy groups of the automorphism group of Kirchberg algebras Søren Eilers (Copenhagen) Semiprojectivity of non-commutative CW-complexes Siegfried Echterhoff (Münster) K-theoretic fibrations (based on joint work with Herve Oyono-Oyono and Ryszard Nest) George Elliott (Toronto) Is classification a chimera? Guihua Gong (Puerto Rico) Geometrization of strong Novikov conjecture for residually finite groups Ilan Hirshberg (Ben Gurion) Finite group actions on the Jiang-Su algebra Masaki Izumi (Kyoto) Classification Z2 actions on the Kirchberg algebras Chunlan Jiang (Hebei Normal) A complete classification of AI algebras and AC structure of AH algebras with ideal property Takeshi Katsura (Toronto) Generic automorphisms of approximately divisible AF algebras satisfy the Rohlin property David Kerr (Texas A&M) Dynamics and perforation Eberhard Kirchberg (Humboldt-Universität zu Berlin) Strong “UC” classes of non-simple C*-algebras Alex Kumjian (Nevada) k-morphs Nadia Larsen (Oslo) Hecke C*-algebras of semidirect products and KMS-states 20 Huaxin Lin (Oregon) Applications of the Elliott program Hiroki Matui (Chiba) Z2 – actions on UHF algebras Ralf Meyer (Göttingen) Computing Kirchberg’s bivariant K-theory Zhuang Niu (Calgary) (Title not available) Narutaka Ozawa (UCLA) Weak amenability of hyperbolic groups Cornel Pasnicu (Puerto Rico) Purely infinite C*-algebras of real rank zero Christopher Phillips (Oregon) Towards Z-stability of direct limits of recursive subhomogeneous C*-algebras Francesc Perera (Autonoma de Barcelona) Representing abstract semigroups as semigroups of projections of C*-algebras Leonel Robert (Fields Institute) Cuntz semi group of ideals and quotients and a generalized Kasparov stabilization theorem Mikael Rørdam (Southern Denmark) The Jiang-Su algebra revisited Klaus Thomsen (Aarhus) On the homoclinic and heteroclinic C*-algebras of expansive dynamical systems Andrew Toms (York) Topological vs. matricial dimension in C*-algebras Wilhelm Winter (Nottingham) Localizing the Elliott conjecture Simon Wassermann (Glasgow) MASAs, tensor products and the extension property Andrew Toms Workshop on Operator Spaces and Quantum Groups December 11–15, 2007 Organizers: Marius Junge (Illinois), Matthias Neufang (Carleton), Vern Paulsen (Houston), Gilles Pisier (Paris and Texas A&M), Zhong-Jin Ruan (Illinois) The aim of this workshop – one of five within the framework of the thematic program on Operator Algebras – was
to bring together researchers working in two very active areas of modern functional analysis which both have their roots in operator algebra theory: the theory of operator spaces and completely bounded maps, on the one hand, and the theory of locally compact quantum groups, on the other hand. The closed self-adjoint subalgebras of the algebra B(H) consisting of all bounded operators on a Hilbert space H can be characterized abstractly via an intrinsic property of the algebra; these (abstract) algebras are called C*-algebras. Any such algebra A inherits naturally the structure of B(H) at each matrix level M n (A) ⊆ B(H n ). A corresponding characterization for closed subspaces of B (H) was given by Z.-J. Ruan (1988) through the formulation of two appropriate conditions on the norms of M n (X) for a Banach space X. The matricially normed spaces satisfying these ‘axioms’ are called (abstract) operator spaces. In the category of operator spaces, the morphisms are operators which respect this matricial structure in a suitable fashion, called completely bounded maps. The richness of the theory stems in particular from the multitude of very different operator space structures that a given Banach space may have, and it thus builds an exciting bridge between Banach spaces and C*-algebras: operator spaces are heading for the C*-world while standing on the ground of Banach spaces. The theory, developed by D.P. Blecher, E.G. Effros, U. Haagerup, M. Junge, V.I. Paulsen, G. Pisier, Z.-J. Ruan, et al., has had considerable impact on the development of functional analysis in different ways. On the one hand, through the solution of longstanding open problems, such as G. Pisier’s solution (1997) to the Halmos problem in operator theory from 1970, and, completing earlier work by Pisier-Shlyakhtenko, Haagerup-Musat’s solution to the Effros-Ruan conjecture from 1991 regarding a Grothendieck-type inequality for jointly completely bounded bilinear forms on C*-algebras; in fact, the latter, presented in M. Musat’s talk, was achieved during the thematic program (cf. G. Elliott’s corresponding article)! On the other hand, a major influence of operator space theory is due to its creation of a suitable framework of ‘non-commutative functional analysis’, which has proven very fruitful for areas such as Banach algebra theory and abstract harmonic analysis. One of the most fundamental themes of the latter field has been the concept of Pontryagin-type duality, and the search for a category that comprises both group algebras, their dual objects as well as other ‘group-like’ structures arising in mathematical physics, such as S.L. Woronowicz’s famous SU q (2). In 2000, J. Kustermans and S. Vaes, building on earlier work by Baaj-Skandalis, Enock-Schwartz and Kac- Thematic Programs Vainerman, presented a simple set of axioms that, as they showed, are powerful enough to yield the above, thereby defining locally compact quantum groups. These are of course neither groups nor locally compact – yet their name is well-deserved since they consist of Hopf-von Neumann algebras M (the co-multiplication replacing the group multiplication) admitting weights (the analogue of left and right Haar measure on a locally compact group) which are invariant under the canonical left and right action of the predual M * on the image of . This theory currently brings together operator algebraists, operator spacers, Banach algebraists, abstract harmonic analysts, and mathematical physicists – indeed, all those – certainly overlapping – groups were present(ing) at the meeting, and we saw a week of very lively discussions between them. To give a concrete example of such a multiple meeting point, we mention the construction – developed in collaborations of Z. Hu, M. Junge, M. Neufang and Z.-J. Ruan (2007) and presented at the meeting by Z. Hu – of certain quantum channels, of interest in quantum information theory, that arise from the representation of the algebra M * = L 1 (G) over a quantum group G as completely bounded maps on B(L 2 (G)), and whose completely bounded minimal entropy can be calculated, in the finite-dimensional setting, by using G. Pisier’s complex interpolation theory for operator spaces. Various natural open questions were discussed in this context during the workshop, e.g., concerning the structure of the fixed point set of these channels, which in turn leads to the concept of non-commutative Poisson boundaries, as presented in R. Tomatsu and S. Vaes’s talks. In summary: an extremely fruitful meeting, on the level of questions as well as answers, and many new bridges built to generate more of both. Speakers: (as listed on program itinerary) Uffe Haagerup (Southern Denmark) Classification of hyperfinite factors up to completely bounded isomorphisms of their preduals Tao Mei (UIUC) Noncommutative H^1 and BMO spaces Timur Oikhberg (Irvine) Representations of Banach algebras as algebras of completely bounded maps Magdalena Musat (Memphis) The Effros-Ruan conjecture for bilinear forms on C¤-algebras Georgios Eleftherakis (Athens) Morita type equivalences for dual operator algebras 21
Page 1: Fields Institute for Research in Ma
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Page 9 and 10: Barbara Keyfitz The FielDS inSTiTuT
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the sum of two proper sub-ideals. B
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Rob Bryce (Brandon) v.5.x: An intro
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community, senior researchers can p
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Ernesto Barrios (ITAM) Bayesian Fac
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notable achievements is his solutio
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of classical Erdos-Renyi models, co
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Workshop on Topological Methods in
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Igor Klep (Ljubljana) Sums of hermi
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The focus of the meeting was the us
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Ilijas Farah (York) Nonseparable UH
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Arafat Tayeb (Centre de Recherche U
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John Phillips (Victoria) An index t
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More information and conference sli
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famous landmarks of Ottawa includin
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Hao Li (Toronto) Equilibria in a so
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Erhan Bayraktar (Michigan) Pricing
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Reinhard Illner (Victoria) From Fok
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Centre for Mathematical Medicine Di
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In Lessons from death: Epidemiologi
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Participants: Michael Milosevic (PM
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Non-Commutative Geometry Organizer:
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Arithmetic Geometry and Number Theo
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AARMS Activities AARMS Summer Schoo
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Commercial/Industrial Mathematics T
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modulated radiation therapy (IMRT)
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To facilitate rapid publication and
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Mathematics Education Ontario Mathe
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designed a sequence of PowerPoint s
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Bob Hallett of Great Big Sea, lates
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Fields Institute Fellows The honour
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Fields Institute Communications Ser
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and Michael Shub, University of Tor
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Members of the Corporation 2007-200
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DAVID JACKSON is a Professor of Mat
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EFIM zELMANOV is the Rita L. Atkins
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Principal Sponsoring Universities 2
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Financial Statements Donors The Fie
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Financial Statements 151
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Acknowledgements The Fields Institu
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