MERT ÇA˘GLAR - İstanbul Kültür Üniversitesi

MERT ÇAĞLAR as of December 2011
Contact
Information
Department of Mathematics and Computer Science Phone: +90 (212) 498 43 58
İstanbul Kültür University Fax: +90 (212) 465 83 10
Ataköy Campus, Bakırköy 34156
E-mail: m.caglar@iku.edu.tr
İstanbul, Turkey
URL: http://web.iku.edu.tr/~mcaglar
Personal
Information
Birth: August 5, 1976
Marital Status: Married
Nationality: Turkish
Gender: Male
Education
Middle East Technical University, Ankara, Turkey
Ph.D. in Mathematics
Dissertation: Invariant subspaces of positive operators on Riesz spaces and
observations on CD 0 (K)-spaces
Advisor: Zafer Ercan
Middle East Technical University, Ankara, Turkey
M.Sc. in Mathematics
Thesis title: Invariant subspaces of positive operators on Banach lattices
Thesis advisor: Zafer Ercan
Marmara University, İstanbul, Turkey
B.S. in Mathematics
Atatürk Lycée, İzmir, Turkey
1991−1994
Collège Saint Joseph, İzmir, Turkey
1987−1991
2001−2005
1999−2001
1994−1998
Employment Associate Professor, İstanbul Kültür University, İstanbul, Turkey 2010−pres.
Assistant Professor, İstanbul Kültür University, İstanbul, Turkey
2005−2010
Research Assistant, Middle East Technical University, Ankara, Turkey
1999−2005
Service
Referee
Turkish Journal of Mathematics, TÜBİTAK, Ankara, Turkey
Reviewer
Nonlinear Analysis: Real World Applications, Elsevier B.V., Amsterdam,
The Netherlands
Administrative
İKÜ Graduate School of Natural Sciences, Executive Board, Member
2010−pres.
Turkish Mathematical Society, Executive Board, Vice-member
2008−2010
Honors and
Awards
Associate Professor title, Inter-University Council (ÜAK), Ankara, Turkey 2010
Graduation with the highest GPA in Mathematics from Marmara University 1998
Memberships Turkish Mathematical Society 2005−pres.
TÜBİTAK Network of Co-operation in Research for Analysis
2008−2010
Foreign
Languages
Erdős Number
English (fluent), French (fluent)
4 : P. Erdős, J.L. Brenner, H.M. Srivastava, M. Nunokawa, M. Çağlar

Research
Interests
Publications
Functional Analysis: operator theory in partially ordered structures, Riesz spaces, and Banach
lattices; especially the invariant subspace problem for positive operators on these spaces.
Complex Analysis: geometric and univalent function theory in one complex variable.
Non-linear Dynamical Systems: chaotic behavior of maps in different systems.
Booklet
Univalent and Geometric Function Theory Seminar Notes, İstanbul Kültür University Press, İstanbul,
2006 (with Y. Polatoğlu, A. Şen, R. Murat Demirer and E. Yavuz).
Research Articles
17. Invariant subspaces of weakly compact-friendly operators, Turkish J. Math., forthcoming (with
T. Mısırlıoğlu).
16. Solution to n-dimensional Sturm-Liouville-like equations using multi-dimensional Schwarzian, J.
Differential Equations 251 (2011), no. 12, 3403-3420 (with M.H. Erkut, S.V. Borisenok and Y.
Polatoğlu).
15. A note on a problem of Abramovich, Aliprantis and Burkinshaw, Positivity 15 (2011), no. 3,
473-480 (with T. Mısırlıoğlu).
14. Coefficient inequality for perturbed harmonic mappings, Appl. Math. Lett. 23 (2010), no. 8,
839-841 (with Y. Polatoğlu and E. Yavuz Duman).
13. Some sufficient conditions for starlikeness and convexity, Turkish J. Math. 34 (2010), no. 3,
333-337 (with M. Nunokawa, S. Owa, Y. Polatoğlu and E. Yavuz Duman).
12. On positive operators without invariant sublattices, Gen. Math. 17 (2009), no. 4, 111-123 (with
U. Gönüllü and T. Mısırlıoğlu).
11. Weakly compact-friendly operators, Vladikavkaz Mat. Zh. 11 (2009), no. 2, 27-30 (with T.
Mısırlıoğlu).
10. The higher-order Schwarzian derivative: its applications for chaotic behavior and new invariant
sufficient condition of chaos, Nonlinear Anal. Real World Appl. 10 (2009), no. 3, 1270-1275
(with G. Hacıbekiroğlu and Y. Polatoğlu).
9. λ-fractional properties of generalized Janowski functions in the unit disc, Mat. Vesnik 60 (2008),
no. 3, 165-171 (with Y. Polatoğlu and E. Yavuz).
8. Multivalued starlike functions of complex order, Acta Univ. Apulensis Math. Inform. 16 (2008),
127-134 (with Y. Polatoğlu, A. Şen, E. Yavuz and S. Owa).
7. Multivalued starlike functions of complex order, Gen. Math. 16 (2008), no. 2, 19-28 (with Y.
Polatoğlu, E. Yavuz and S. Owa).
6. Multivalued p-valent starlike functions, Math. Balkanica 21 (2007), no. 3-4, 389-398 (with Y.
Polatoğlu, A. Şen, E. Yavuz and S. Owa).
5. Invariant subspaces for positive operators on locally convex solid Riesz spaces, Indag. Math. 18
(2007), no. 3, 417-420 (with Z. Ercan).

4. On Janowski starlike functions, J. Inequal. Appl. (2007), Art. ID 14630, 10 pp. (with Y. Polatoğlu,
A. Şen, E. Yavuz and S. Owa).
3. New distortion theorems for Sakaguchi functions, Math. Inequal. Appl. 10 (2007), no. 4, 869-874
(with Y. Polatoğlu).
2. Inequalities for the Schwarzian derivative for subclasses of convex functions in the unit disc,
Vladikavkaz Mat. Zh. 8 (2006), no. 2, 50-53 (with Y. Polatoğlu and A. Şen).
1. Generalized Alexandroff duplicates and CD 0 (K)-spaces, Cent. Eur. J. Math. 4 (2006), no. 3,
371-375 (with Z. Ercan and F. Polat).
Conference Proceedings
5. Positive operators on Hilbert lattices, Acta Univ. Apulensis Math. Inform. (2009), 685-689 (with
Ö. Çavuşoğlu and T. Mısırlıoğlu). Special issue of the International Conference on Theory and
Applications in Mathematics and Informatics, Alba Iulia, Romania, 2009.
4. A new non-linear filter design for the detection of phase transitions in ECoG data (with R.
Kozma, Y. Polatoğlu and R. Murat Demirer), Proceedings of the International Joint Conference
on Neural Networks, Atlanta, Ga, USA, (2009), 671-676.
3. A technical note on a result of Y.A. Abramovich, C.D. Aliprantis, G. Sirotkin and V.G. Troitsky,
Proceedings of the International Symposium on New Development of Geometric Function Theory
and its Applications, National University of Malaysia, (2008), 335-338.
2. Schwarzian derivative revisited, Journal of İstanbul Kültür University 4 (2006), no. 4, 139-143
(with Y. Polatoğlu and R. Murat Demirer). Special issue of the international conference Chaos
and Complex Systems I, İstanbul Kültür University, İstanbul, 2006.
1. Does a chaotic system dynamic really exist in nature or is it a misconception dynamics: a hypothesis,
Journal of İstanbul Kültür University 4 (2006), no. 4, 223-230 (with R. Murat Demirer,
Y. Polatoğlu and O. Demirer). Special issue of the international conference Chaos and Complex
Systems I, İstanbul Kültür University, İstanbul, 2006.
Papers in Preparation
1. Growth and distortion theorems for multivalent close-to-convex harmonic functions (with Y. Polatoğlu
and T. Mısırlıoğlu), submitted.
Addresses
Plenary Talks
14. Invariant Subspaces of Weakly Compact-friendly Operators
Conference on Ordered Spaces and Applications,
National Technical University of Athens, Athens, Greece 2011
13. Positive Quasi-similarity and Invariant Subspaces
Order Analysis and Related Problems of Mathematical Modelling,
South Mathematical Institute, Vladikavkaz, Russia 2010
12. Positive Operators on Hilbert Lattices
International Conference on Theory and Applications in Mathematics and Informatics,
Alba Iulia, Romania 2009

11. On Positive Operators Without Invariant Sublattices
Geometric Function Theory and Applications, Sibiu, Romania 2009
10. Domination of Lattice Homomorphisms
Analysis and Theory of Functions, İstanbul Kültür University, İstanbul, Turkey 2009
9. Domination of Lattice Homomorphisms
Positivity VI, El Escorial, Madrid, Spain 2009
8. A Technical Note on a Result of Y.A. Abramovich, C.D. Aliprantis, G. Sirotkin and
V.G. Troitsky
International Symposium on New Development of Geometric Function Theory
and its Applications, National University of Malaysia, Bangi, Selangor, Malaysia 2008
7. Weakly Compact-Friendly Operators
A Symposium on Positivity and its Applications in Science and Economics,
Abant İzzet Baysal University, Bolu, Turkey 2008
6. Two Problems Concerning Invariant Subspaces of Positive Operators
International Conference on Theory and Applications in Mathematics and Informatics,
Alba Iulia, Romania 2007
5. Invariant Subspaces for Semigroups of Operators on Locally Convex-Solid Riesz Spaces
International Symposium on Complex Analysis, Sibiu, Romania 2007
4. A Solution to a Problem of Abramovich, Aliprantis and Burkinshaw
Geometric Function Theory and Applications, İstanbul Kültür University, İstanbul 2007
3. On a Problem of Abramovich, Aliprantis and Burkinshaw
Positivity V, Queen’s University of Belfast, Northern Ireland 2007
2. Chaotic Behavior of Maps in Different Set-Theoretic Universes
Order Analysis and Related Problems of Mathematical Modelling,
Vladikavkaz Scientific Center, Vladikavkaz, Russia 2006
1. Schwarzian Derivative for Several-Variabled Maps and Geometric Interpretations
Chaos and Complex Systems I, İstanbul Kültür University, İstanbul 2006
Colloquium and Seminar Talks
15. Compact-friendly-like Operators: Some Recent Advances
General Seminar, Mathematics Department, Atılım University, Ankara 2011
14. Positive Quasi-similarity and Invariant Subspaces
Positivity Seminars, Mathematics Department, Abant İBÜ, Bolu 2011
13. The Invariant Subspace Problem in Perspective
Mathematics Colloquia, Sabancı University, FENS, İstanbul 2011
12. On Positive Operators Without Invariant Sublattices
İstanbul Analysis Seminars, Sabancı University, Karaköy Communication Center, İstanbul 2009

11. Nuclear Fréchet Lattices
İstanbul Analysis Seminars, Sabancı University, Karaköy Communication Center, İstanbul 2008
10. Variations on Compact-Friendliness
İstanbul Analysis Seminars, Sabancı University, Karaköy Communication Center, İstanbul 2008
9. A Solution to a Problem of Abramovich, Aliprantis and Burkinshaw
İstanbul Analysis Seminars, Sabancı University, Karaköy Communication Center, İstanbul 2007
8. The Invariant Subspace Problem: A Smorgasbord of Perspectives
İstanbul Analysis Seminars, Sabancı University, Karaköy Communication Center, İstanbul 2007
7. Gowers’s Solution to Banach’s Hyperplane Problem
General Seminar, Department of Mathematics and Computer Science,
İstanbul Kültür University, İstanbul 2006
6. Invariant Subspaces for Positive Operators on Riesz Spaces and Observations
on CD 0 (K)-Spaces
İstanbul Analysis Seminars, Sabancı University, Karaköy Communication Center, İstanbul 2005
5. The Invariant Subspace Problem: History and Some Recent Advances
General Seminar, Department of Mathematics and Computer Science,
İstanbul Kültür University, İstanbul 2005
4. Some Open Problems and Conjectures Associated with the Invariant Subspace Problem
Positivity Seminars, Mathematics Department, METU, Ankara 2004
3. Invariant Subspaces for Positive Operators on Locally Solid Riesz Spaces
Positivity Seminars, Mathematics Department, METU, Ankara 2004
2. Lomonosov’s Invariant Subspace Theorem for Multivalued Linear Operators 2004
Linear Topological Spaces and Complex Analysis Seminar, Mathematics Department,
METU, Ankara 2004
1. The Invariant Subspace Problem for Positive Operators on Banach Lattices
General Seminar, Mathematics Department, METU, Ankara 2003
Organizations
İstanbul Analysis Seminars
Sabancı University, Karaköy Communication Center, İstanbul
Joint organizer
2005−pres.
Graduate Summer School on Geometric Function Theory
August 16-25, 2010, İstanbul Kültür University
Joint organizer 2010
Analysis and Theory of Functions−Nâzım Terzioğlu Memorial Symposium
August 24-26, 2009, İstanbul Kültür University
Joint organizer 2009
Geometric Function Theory and Applications (GFTA 2007)
August 20-24, 2007, İstanbul Kültür University
Vice-organizer 2007

Projects
Courses Taught
Establishment of National CORS (Continuously Operating Reference Stations)
System and Determination of Datum Transformation Parameters
The Scientific and Technological Research Council of Turkey
TÜBİTAK Project No: 1007 105G017
Researcher of the Executive Institution (İstanbul Kültür University) 2006-2009
Undergraduate
Calculus I, II, III, IV; Complementary Calculus; Analysis III, IV; Topology;
Probability and Statistics (Department of Mathematics and Computer Science);
Introduction to Probability Theory and Statistics (Department of Computer Engineering);
Differential Equations I, II (Department of Mathematics and Computer Science);
Linear Algebra (Department of Industrial Engineering)
Graduate
Real Analysis; General Topology; Functional Analysis; Topological Vector Spaces;
Positive Operators and Banach Lattices; Selected Topics in Topology I, II;
Selected Topics in Analysis II; Selected Topics in Operator Theory
Postgraduate
Supervision
Invariant Subspaces of Positive Operators on Banach C(K)-modules
Uğur Gönüllü
Ph.D. Thesis, İstanbul Kültür University
2008−pres.
Co-supervisor: Anatoly G. Kusraev
Multi-norms
Mehmet Selçuk Türer
M.Sc. Thesis, İstanbul Kültür University
2008−2010
Positive Operators on Banach Lattices
Özlem Çavuşoğlu
M.Sc. Thesis, İstanbul Kültür University
2006−2008
Co-supervisor: R. Tunç Mısırlıoğlu
Pozitif Operatörler için Değişmez Alt-Örgüler
Uğur Gönüllü
M.Sc. Thesis, İstanbul Kültür University
2006−2008
Co-supervisor: R. Tunç Mısırlıoğlu
Operatör Yarı-Gruplarının Değişmez Alt-Uzayları
Canan Kaya
M.Sc. Thesis, İstanbul Kültür University
2006−2008
Co-supervisor: R. Tunç Mısırlıoğlu
Her Yerde Sürekli Olan Hiçbir Yerde Türevi Olmayan Fonksiyonlar
Begüm Çalışkan
Senior’s Thesis, İstanbul Kültür University 2011
Fonksiyon Genişlemeleri
Aygün Belin Temiz
Senior’s Thesis, İstanbul Kültür University 2007

References
(available upon
request)
Prof. Dr. Şafak Alpay
Department of Mathematics, Middle East Technical University, Ankara, Turkey
Prof. Dr. Aydın Aytuna
Faculty of Engineering and Natural Sciences, Sabancı University, İstanbul, Turkey
Prof. Dr. Zafer Ercan
Department of Mathematics, Abant İzzet Baysal University, Bolu, Turkey