Tr, Eng

        Welcome to  YILDIRAY OZAN's Personal Home Page


Book: Türevlenebilir Manifoldlara Giriş (Preface)




 (Available form Odtüden, Important note: The book is soft cover unlike the picture above suggests.) 

Corrections to the first edition as of  September 22, 2017

Corrected Symbol List and Index



2022 Spring Semester

Math 371: Differential Geometry (Youtube) (Youtube Video Notes) Video Content List Syllabus

Math 505: Differentiable Manifolds  (Youtube) (Youtube Video Notes) Video Content List


2021 Fall Semester

Math 341: Graph Theory (Youtube) (Youtube Video Notes) Video Content List Syllabus

Math 401: Probability Theory  (Youtube) (Youtube Video Notes) Video Content List Syllabus



2021 Summer

Math 254: Differential Equations (Youtube) (Youtube Video Notes) Video Content List

Math 420:  Topology (Youtube) (Youtube Video Notes) Video Content List


2021 Spring Semester

Math 538: Algebraic Topology II  (Youtube) (Youtube Video Notları) Video Contents

Math 424: Galois Theory of Coverings and Linear Differential Equations (Youtube) (Youtube Video Notları) Video Contents


2020 Fall Semester

Math 537: Algebraic Topology I  (Youtube) (Youtube Video Notları) Video Contents

Math 349: Introduction to Analysis (Youtube) (Youtube Video Notları) Video Contents Exercises

                   Recitation Videos Play List by Sadık Terzi


2020 Spring Semester

Math 709: Differentiable Manifolds and Vector Bundles (Lecture Notes and Videos) (Youtube) (Youtube Video Notes 1-24) (25-36) (37-57) Video Contents

Math 371: Differential Geometry (Videos) (Notes) (Video Lecture Notes)

Research Interests

Topology of Real Algebraic Varieties and Symplectic - Contact Topology

Education History

Bs.   METU Mathematics Dept., 1989

Ph.D. Michigan State University, 1994

Publications and Preprints (available upon request)


1.  Equivariant Picard Groups of the Moduli Spaces of Some Finite Abelian Covers of The Riemann Sphere, Topology and Its Applicaitons, vol. 326, 1March 2023, 108429,

2. (Joint with F. Atalan ve E. Medetoğulları) Liftable homeomorphisms of cyclic and rank two finite abelian branched covers over the real projective plane, Topology and Its Applicaitons, vol. 288, February 2021,

3. (Joint with F. Atalan ve E. Medetoğulları) Liftable homeomorphisms of rank two finite abelian branched covers,  Archiv der Mathematik,  116 (2021), 3748, doi:

4. (Aram Bingham ve Mahir Bilen Can ile ortak) A Filtration on Equivairant Borel-Moore  Homology, Forum Math. Sigma 7 (2019), e18, 13 pp.

 5. On Cohomology of Invariant Submanifolds of Hamiltonian Actions, Michigan Math. J.   53 (2005), no. 3, 579-584.

 6.  Relative Flux Homomorphism in Symplectic Geometry, Proc. Amer. Math. Soc.
       133 (2005), no. 4, 1223-1230.

  7. On Homotopy Groups of Real Algebraic Varieties and Their Complexifications, Geom. Dedicata, 108 (2004), no.1, 131-140.

  8.  Relative Topology of Real Algebraic Varieities in Their Complexifications, Pacific J. Math. 217 (2004), no. 2, 291-302.

  9.  On Algebraic K-Theory of Real Algebraic Varieties, J. Pure and Appl. Algebra 170 (2002), no. 2-3, 287-293.

 10.  On Entire Rational Maps of Real Surfaces, J. Korean Math. Soc. 39 (2002), no. 1, 77-89.

 11.  On Homology of Real Algebraic Sets, Proc. Amer. Math. Soc. 129 (2001), no. 11, 3167-3175.

  12.  (Arzu Çelikten’le ortak), An Obstruction to Finding Algebraic Models for Smooth
       Manifolds with Prescribed Algebraic Submanifolds, Math. Proc. Cambridge Philos. Soc.
       130 (2001), no. 2, 281-286.

  13.  Homology of Real Algebraic Fiber Bundles Having Circle as Fiber or Base, Michigan Math.  Journal, 46 (1999), 113-121.

  14.  Characteristic Classes and Algebraic Homology of Real Algebraic Varieties, Proceedings of the 11. Türk Matematik Kongresi, Isparta, Türkiye, 7-11 Eylül  1998. Süleyman Demirel Üniversitesi Basimevi, Isparta, 1999, 81-84.pdf

  15. Quotients of Real Algebraic Sets via Finite Groups, Turkish Journal of Mathematics, 21 (1997), 493-499.

  16. On Entire Rational Maps in Real Algebraic Geometry, Michigan Math. Journal, 42 (1995), 141-145.

  17.  Real Algebraic Principal Fibrations, AMS. Contemporary Mathematics, Volume 182 (1995), 121-134.

  18. Trace Homomorphism for Smooth Manifolds pdf

  19.  Triviality of Symplectic SU(2)-actions on Homology, MSRI preprint series #2004-004.pdf

  20.  Homology of Non Orientable Real Algebraic Varieties (preprint)pdf

  21.  (J. Huisman’la ortak) Real Algebraic Differential Forms On Real Algebraic Varieties (preprint)pdf

A Geometry Topology Talk for Students (Mersin Univ. 2012)  17/10/2017

Seminar Notes on Milnor’s Exotic Spheres 10/20/2017

Algebraic Topology Summer School Lecture Notes 21/06/2016

Simplectic Topology Workshop Notes ( Atılım Univ. Sept. 2016) 10/19/2017

Seminar Notes on Arf Invariant 01/10/2016

Grassmannians Lecture Notes (Turkish)  09/06/2017


Galois Theory, Covering Spaces ve Differential Equations (Hacettepe Üniv., Turkish) 09/11/2017,  Computer Presentation




Contact Information

Middle East Technical University
Mathematics Department
06800 Ankara

Office place: M-217

Phone: +90 312-210 5373

Fax: +90 312-210 2972