˘
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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