˘ MERT C ¸ AGLAR as of June 2014 Department of Mathematics and Computer Science ˙ Istanbul K¨ ult¨ ur University Atak¨ oy Campus, Bakırk¨ oy 34156 ˙ Istanbul, Turkey T 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 CD0 (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, Istanbul, Turkey B.S. in Mathematics ˙ Atat¨ urk Lyc´ ee, Izmir, Turkey ˙ Coll` ege Saint Joseph, Izmir, Turkey 1999−2001 Employment ˙ ˙ Associate Professor, Istanbul K¨ ult¨ ur University, Istanbul, Turkey ˙ ˙ Assistant Professor, Istanbul K¨ ult¨ ur University, Istanbul, Turkey Research Assistant, Middle East Technical University, Ankara, Turkey 2010−pres. 2005−2010 1999−2005 Service Referee Filomat, University of Niˇs, Niˇs, Serbia Positivity, Birkh¨ auser Verlag, Basel, Switzerland ¨ ITAK, ˙ Turkish Journal of Mathematics, TUB Ankara, Turkey Contact Information +90 (212) 498 43 58 u +90 (212) 465 83 10 k Ï [email protected] http://web.iku.edu.tr/~mcaglar 2001−2005 1994−1998 1991−1994 1987−1991 Reviewer The Netherlands Organization for Scientific Research (NWO), Den Haag, NL ¨ ITAK ˙ TUB Academic Research Funding Programs (ARDEB), Ankara, TR UEFISCDI, Bucharest, RO Administrative ˙ U ¨ Faculty of Science and Letters, Vice-dean IK ˙ U ¨ Faculty of Science and Letters, Faculty Board, Member IK ˙ U ¨ Faculty of Science and Letters, Executive Board, Member IK ˙ U ¨ Institute of Sciences, Executive Board, Member IK Turkish Mathematical Society, Executive Board, Vice-member Honors and Awards ¨ Associate Professor title, Inter-University Council (UAK), Ankara, Turkey Graduation with the highest GPA in Mathematics from Marmara University Memberships Turkish Mathematical Society ¨ ITAK ˙ TUB Doctoral and Post-doctoral Network Foreign Languages English, French ˝ s Number Erdo 4 : P. Erd˝ os, J.L. Brenner, H.M. Srivastava, M. Nunokawa, M. C ¸ a˘glar 2012−pres. 2012−pres. 2012−pres. 2010−pres. 2008−2010 2010 1998 2005−pres. 2008−2012 Research Interests 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. Publications Booklet ˙ Univalent and Geometric Function Theory Seminar Notes, Istanbul K¨ ult¨ ur University Press, ˙Istanbul, 2006 (with Y. Polato˘glu, A. S¸en, 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. Mısırlıo˘ glu). 16. A note on a problem of Abramovich, Aliprantis and Burkinshaw, Positivity 15 (2011), no. 3, 473-480 (with T. Mısırlıo˘ glu). 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. Polato˘ glu). 14. Coefficient inequality for perturbed harmonic mappings, Appl. Math. Lett. 23 (2010), no. 8, 839-841 (with Y. Polato˘ glu 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. Polato˘glu and E. Yavuz Duman). 12. On positive operators without invariant sublattices, Gen. Math. 17 (2009), no. 4, 111-123 (with U. G¨ on¨ ull¨ u and T. Mısırlıo˘glu). 11. Weakly compact-friendly operators, Vladikavkaz Mat. Zh. 11 (2009), no. 2, 27-30 (with T. Mısırlıo˘ glu). 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. Hacıbekiro˘ glu and Y. Polato˘glu). 9. λ-fractional properties of generalized Janowski functions in the unit disc, Mat. Vesnik 60 (2008), no. 3, 165-171 (with Y. Polato˘glu and E. Yavuz). 8. Multivalued starlike functions of complex order, Acta Univ. Apulensis Math. Inform. 16 (2008), 127-134 (with Y. Polato˘ glu, A. S¸en, E. Yavuz and S. Owa). 7. Multivalued starlike functions of complex order, Gen. Math. 16 (2008), no. 2, 19-28 (with Y. Polato˘ glu, E. Yavuz and S. Owa). 6. Multivalued p-valent starlike functions, Math. Balkanica (N.S.) 21 (2007), no. 3-4, 389-398 (with Y. Polato˘ glu, A. S ¸ en, 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. Polato˘ glu, A. S ¸ en, E. Yavuz and S. Owa). 3. New distortion theorems for Sakaguchi functions, Math. Inequal. Appl. 10 (2007), no. 4, 869-874 (with Y. Polato˘ glu). 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. Polato˘glu and A. S¸en). 1. Generalized Alexandroff duplicates and CD0 (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 ¨ C O. ¸ avu¸so˘ glu and T. Mısırlıo˘glu). 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. Polato˘ glu 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 Istanbul K¨ ult¨ ur University 4 (2006), no. 4, 139-143 (with Y. Polato˘ glu and R. Murat Demirer). Special issue of the international conference Chaos ˙ ˙ and Complex Systems I, Istanbul K¨ ult¨ ur University, Istanbul, 2006. 1. Does a chaotic system dynamic really exist in nature or is it a misconception dynamics: a hy˙ pothesis, Journal of Istanbul K¨ ult¨ ur University 4 (2006), no. 4, 223-230 (with R. Murat Demirer, Y. Polato˘ glu and O. Demirer). Special issue of the international conference Chaos and Complex ˙ ˙ Systems I, Istanbul K¨ ult¨ ur University, Istanbul, 2006. Educational Articles 2. e ve π sayıları kesirli de˘ gildir, Matematik D¨ unyası, 2014-I, 37-39 (with Z. Ercan). 1. D¨ uzg¨ un sınırlılık ilkesi, Matematik D¨ unyası, 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 Terzio˘glu TT-70 Fest: On the Occasion of Tosun Terzio˘glu’s 70th Birthday ˙ Sabancı University, Karak¨ oy Communication Center, Istanbul 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, Istanbul K¨ ult¨ ur University, Istanbul, 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 Izzet 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, Istanbul K¨ ult¨ ur University, Istanbul 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, Istanbul K¨ ult¨ ur University, Istanbul 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, Istanbul 2014 19. Mean Ergodic Operators on Banach and Fr´echet Lattices Mini-course: Introduction to Dynamics of Linear Operators ˙ ˙ Istanbul Analysis Seminars, Sabancı University, Karak¨oy Communication Center, Istanbul 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 ˙ U, ¨ Bolu Positivity Seminars, Mathematics Department, Abant IB 2012 16. Invariant Subspaces of Compact-friendly-like Operators: The State-of-the-art and Some Open Problems ˙ ˙ Istanbul Analysis Seminars, Sabancı University, Karak¨oy Communication Center, Istanbul 2011 15. Compact-friendly-like Operators: Some Recent Advances General Seminar, Mathematics Department, Atılım University, Ankara 2011 14. Positive Quasi-similarity and Invariant Subspaces ˙ U, ¨ Bolu Positivity Seminars, Mathematics Department, Abant IB 2011 13. The Invariant Subspace Problem in Perspective ˙ Mathematics Colloquia, Sabancı University, FENS, Istanbul 2011 12. On Positive Operators Without Invariant Sublattices ˙ ˙ Istanbul Analysis Seminars, Sabancı University, Karak¨oy Communication Center, Istanbul 2009 11. Nuclear Fr´echet Lattices ˙ ˙ Istanbul Analysis Seminars, Sabancı University, Karak¨oy Communication Center, Istanbul 2008 10. Variations on Compact-Friendliness ˙ ˙ Istanbul Analysis Seminars, Sabancı University, Karak¨oy Communication Center, Istanbul 2008 9. A Solution to a Problem of Abramovich, Aliprantis and Burkinshaw ˙ ˙ Istanbul Analysis Seminars, Sabancı University, Karak¨oy Communication Center, Istanbul 2007 8. The Invariant Subspace Problem: A Smorgasbord of Perspectives ˙ ˙ Istanbul Analysis Seminars, Sabancı University, Karak¨oy Communication Center, Istanbul 2007 7. Gowers’s Solution to Banach’s Hyperplane Problem General Seminar, Department of Mathematics and Computer Science, ˙ ˙ Istanbul K¨ ult¨ ur University, Istanbul 2006 6. Invariant Subspaces for Positive Operators on Riesz Spaces and Observations on CD0 (K)-Spaces ˙ ˙ Istanbul Analysis Seminars, Sabancı University, Karak¨oy Communication Center, Istanbul 2005 5. The Invariant Subspace Problem: History and Some Recent Advances General Seminar, Department of Mathematics and Computer Science, ˙ ˙ Istanbul K¨ ult¨ ur University, Istanbul 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 Linear Topological Spaces and Complex Analysis Seminar, Mathematics Department, METU, Ankara 1. The Invariant Subspace Problem for Positive Operators on Banach Lattices General Seminar, Mathematics Department, METU, Ankara 2004 2004 2003 Organizations Projects Courses Taught ˙Istanbul Analysis Seminars ˙ Sabancı University, Karak¨ oy Communication Center, Istanbul Joint organizer 2005−pres. Turkish-Japanese Joint Symposium on Function Theory and its Applications ˙ September 3-6, 2012, Istanbul K¨ ult¨ ur University Joint organizer 2012 Graduate Summer School on Geometric Function Theory ˙ August 16-25, 2010, Istanbul K¨ ult¨ ur University Joint organizer 2010 Analysis and Theory of Functions−Nˆazım Terzio˘glu Memorial Symposium ˙ August 24-26, 2009, Istanbul K¨ ult¨ ur University Joint organizer 2009 Geometric Function Theory and Applications (GFTA 2007) ˙ August 20-24, 2007, Istanbul K¨ ult¨ ur University Vice-organizer 2007 ˙Istanbul Analysis Seminars The Scientific and Technological Research Council of Turkey ¨ ITAK-B ˙ ˙ TUB IDEB 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 ¨ ITAK ˙ TUB Project No: 1007 105G017 ˙ Researcher of the Executive Institution (Istanbul K¨ ult¨ ur University) 2006-2009 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] Tu˘ gc¸en Selmano˘ gulları Ph.D. Thesis, Mimar Sinan Fine Arts University 2013−pres. Martingales in Banach Lattices Mehmet Sel¸cuk T¨ urer ˙ Ph.D. Thesis, Istanbul K¨ ult¨ ur University 2010−pres. Cyclically Compact Operators on Kaplansky-Hilbert Modules U˘ gur G¨ on¨ ull¨ u ˙ Ph.D. Thesis, Istanbul K¨ ult¨ ur University Co-supervisor: Anatoly G. Kusraev 2008−2014 Banach Lattices on Which Every Bounded Linear Operator is Regular Nazlı Do˘ gan ˙ M.Sc. Thesis, Istanbul K¨ ult¨ ur University 2011−2013 Multi-norms Mehmet Sel¸cuk T¨ urer ˙ M.Sc. Thesis, Istanbul K¨ ult¨ ur University 2008−2010 Positive Operators on Banach Lattices ¨ Ozlem C ¸ avu¸so˘ glu ˙ M.Sc. Thesis, Istanbul K¨ ult¨ ur University 2006−2008 ¨ uler Pozitif Operat¨ orler i¸cin De˘ gi¸smez Alt-Org¨ [Invariant Sublattices for Positive Operators] U˘ gur G¨ on¨ ull¨ u ˙ M.Sc. Thesis, Istanbul K¨ ult¨ ur University 2006−2008 Operat¨ or Yarı-Gruplarının De˘ gi¸smez Alt-Uzayları [Invariant Subspaces of Operator Semigroups] Canan Kaya ˙ M.Sc. Thesis, Istanbul K¨ ult¨ ur University 2006−2008 ¨ Manifoldlar Uzerinde Stokes Teoremi [Stokes’ Theorem on Manifolds] Ay¸senur Altunsoy ˙ Senior’s Thesis, Istanbul K¨ ult¨ ur University 2013 Boole Cebirlerinde Stone Teoremi [Stone’s Theorem in Boolean Algebras] S¨ umeyya Tu˘ g¸ce Arar ˙ Senior’s Thesis, Istanbul K¨ ult¨ ur University 2013 Kaydırma, C ¸ arpım, ve Volterra Operat¨orleri [Shift, Multiplication, and Volterra Operators] C ¸ i˘ gdem C ¸ elik ˙ Senior’s Thesis, Istanbul K¨ ult¨ ur University 2012 Modern Osmanlı Matemati˘ gi [Modern Ottoman Mathematics] Filiz Gizem Topuz ˙ Senior’s Thesis, Istanbul K¨ ult¨ ur University 2012 Her Yerde S¨ urekli Olan Hi¸cbir Yerde T¨ urevi Olmayan Fonksiyonlar [Continuous Nowhere Differentiable Functions] Beg¨ um C ¸ alı¸skan ˙ Senior’s Thesis, Istanbul K¨ ult¨ ur University 2011 Fonksiyon Geni¸slemeleri [Extensions of Functions] Ayg¨ un Belin Temiz ˙ Senior’s Thesis, Istanbul K¨ ult¨ ur University 2007 References (available upon request) Prof. Dr. S ¸ afak Alpay Department of Mathematics, Middle East Technical University, Ankara, Turkey Prof. Dr. Aydın Aytuna ˙ Faculty of Engineering and Natural Sciences, Sabancı University, Istanbul, Turkey Prof. Dr. Zafer Ercan ˙ Department of Mathematics, Abant Izzet Baysal University, Bolu, Turkey

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