MERT ÇAĞLAR as of June 2014

MERT ÇAĞLAR as of June 2014 Contact Information Department of Mathematics and Computer Science T +90 (212) 498 43 58 İstanbul Kültür University u +90 (212) 465 83 10 Ataköy Campus, Bakırköy 34156 k m.caglar@iku.edu.tr İstanbul, Turkey Ï 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 Filomat, University of Niš, Niš, Serbia Positivity, Birkhäuser Verlag, Basel, Switzerland Turkish Journal of Mathematics, TÜBİTAK, Ankara, Turkey Reviewer The Netherlands Organization for Scientific Research (NWO), Den Haag, NL TÜBİTAK Academic Research Funding Programs (ARDEB), Ankara, TR UEFISCDI, Bucharest, RO Administrative İKÜ Faculty of Science and Letters, Vice-dean 2012 pres. İKÜ Faculty of Science and Letters, Faculty Board, Member 2012 pres. İKÜ Faculty of Science and Letters, Executive Board, Member 2012 pres. İKÜ Institute of 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 Doctoral and Post-doctoral Network 2008 2012 Foreign Languages Erdős Number English, French 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 19. Every norm is a restriction of an order-unit norm (with Z. Ercan), submitted. 18. Order-unit-metric spaces, Positivity, forthcoming (with Z. Ercan). 17. Invariant subspaces of weakly compact-friendly operators, Turkish J. Math. 36 (2012), no. 2, 291-295 (with T. Mısırlıoğlu). 16. A note on a problem of Abramovich, Aliprantis and Burkinshaw, Positivity 15 (2011), no. 3, 473-480 (with T. Mısırlıoğlu). 15. 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). 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 (N.S.) 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. (N.S.) 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. Educational Articles 2. e ve π sayıları kesirli değildir, Matematik Dünyası, 2014-I, 37-39 (with Z. Ercan). 1. Düzgün sınırlılık ilkesi, Matematik Dünyası, 2013-III, 73-75 (with Z. Ercan). Addresses Plenary Talks 16. Order-unit-metric Spaces Positivity VII: Zaanen Centennial Conference Leiden University, The Netherlands 2013 15. Standing on One s Own Feet : Reflections on Tosun Terzioğlu TT-70 Fest: On the Occasion of Tosun Terzioğlu s 70 th Birthday Sabancı University, Karaköy Communication Center, İstanbul 2012 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 1 Decembrie 1918 University of Alba Iulia, Alba Iulia, Romania 2009 11. On Positive Operators Without Invariant Sublattices Geometric Function Theory and Applications University Lucian Blaga of Sibiu, 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 1 Decembrie 1918 University of Alba Iulia, Alba Iulia, Romania 2007 5. Invariant Subspaces for Semigroups of Operators on Locally Convex-Solid Riesz Spaces International Symposium on Complex Analysis University Lucian Blaga of Sibiu, 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 Functions of Several Variables and Geometric Interpretations Chaos and Complex Systems I, İstanbul Kültür University, İstanbul 2006 Colloquium and Seminar Talks 20. The Invariant Subspace Problem via Compact-friendly-like Operators: A Survey General Seminar, Mathematics Department, Mimar Sinan Fine Arts University, İstanbul 2014 19. Mean Ergodic Operators on Banach and Fréchet Lattices Mini-course: Introduction to Dynamics of Linear Operators İstanbul Analysis Seminars, Sabancı University, Karaköy Communication Center, İstanbul 2012 18. Invariant Subspaces of Compact-friendly-like Operators and Associated Problems General Seminar, Mathematics Department, Hacettepe University, Ankara 2012

17. Compact-friendly-like Operators and Related Problems Positivity Seminars, Mathematics Department, Abant İBÜ, Bolu 2012 16. Invariant Subspaces of Compact-friendly-like Operators: The State-of-the-art and Some Open Problems İstanbul Analysis Seminars, Sabancı University, Karaköy Communication Center, İstanbul 2011 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. Turkish-Japanese Joint Symposium on Function Theory and its Applications September 3-6, 2012, İstanbul Kültür University Joint organizer 2012 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 İstanbul Analysis Seminars The Scientific and Technological Research Council of Turkey TÜBİTAK-BİDEB 2217 Chief Executive of the Programme 2013-pres. 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 Courses Taught Undergraduate Calculus I, II, III, IV; Complementary Calculus; Analysis III, IV; Topology; Probability and Statistics (Department of Mathematics and Computer Science); Differential Equations I, II (Department of Mathematics and Computer Science); Introduction to Probability Theory and Statistics (Department of Computer Engineering); Linear Algebra (Arel University, Department of Industrial Engineering); Introduction to Probability and Statistics (Sabancı University, FENS); Inverse and Implicit Function Theorems and Applications (Nesin Mathematics Village). Graduate Real Analysis; General Topology; Methods of 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; Riesz Spaces (Nesin Mathematics Village). Postgraduate Supervision [To be decided] Tuğçen Selmanoğulları Ph.D. Thesis, Mimar Sinan Fine Arts University Martingales in Banach Lattices Mehmet Selçuk Türer Ph.D. Thesis, İstanbul Kültür University 2010 pres. 2013 pres.

Cyclically Compact Operators on Kaplansky-Hilbert Modules Uğur Gönüllü Ph.D. Thesis, İstanbul Kültür University 2008 2014 Co-supervisor: Anatoly G. Kusraev Banach Lattices on Which Every Bounded Linear Operator is Regular Nazlı Doğan 2011 2013 Multi-norms Mehmet Selçuk Türer 2008 2010 Positive Operators on Banach Lattices Özlem Çavuşoğlu 2006 2008 Pozitif Operatörler için Değişmez Alt-Örgüler [Invariant Sublattices for Positive Operators] Uğur Gönüllü 2006 2008 Operatör Yarı-Gruplarının Değişmez Alt-Uzayları [Invariant Subspaces of Operator Semigroups] Canan Kaya 2006 2008 Manifoldlar Üzerinde Stokes Teoremi [Stokes Theorem on Manifolds] Ayşenur Altunsoy Senior s Thesis, İstanbul Kültür University 2013 Boole Cebirlerinde Stone Teoremi [Stone s Theorem in Boolean Algebras] Sümeyya Tuğçe Arar Senior s Thesis, İstanbul Kültür University 2013 Kaydırma, Çarpım, ve Volterra Operatörleri [Shift, Multiplication, and Volterra Operators] Çiğdem Çelik Senior s Thesis, İstanbul Kültür University 2012 Modern Osmanlı Matematiği [Modern Ottoman Mathematics] Filiz Gizem Topuz Senior s Thesis, İstanbul Kültür University 2012 Her Yerde Sürekli Olan Hiçbir Yerde Türevi Olmayan Fonksiyonlar [Continuous Nowhere Differentiable Functions] Begüm Çalışkan Senior s Thesis, İstanbul Kültür University 2011 Fonksiyon Genişlemeleri [Extensions of Functions] 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