Geometry helps us understand the architecture of the Earth locally and the Cosmos globally, where order and chaos are interconnected, designed by the Creator as a guide for us. E.G.
I completed my Ph.D. in Mathematics at Ankara University, under the supervision of Hasan Hilmi Hacisalihoglu and Yusuf Yayli.
My research focuses on differential geometry, with particular emphasis on the study of Weierstrass-Enneper representations, the Laplace-Beltrami operator, and the Cheng-Yau operator for helicoidal, rotational, minimal, maximal, and non-orientable surfaces and hypersurfaces in space forms. I also investigate their curvatures, derive parametric (explicit) and algebraic (implicit) equations for these surfaces and hypersurfaces, and transform them into 3D visualizations.
Some of my colleagues with whom I have collaborated on various papers include Bang-Yen Chen, Hasan Hilmi Hacisalihoglu, Yusuf Yayli, Yanlin Li, Young-Ho Kim, Martin Magid, Magdalena Toda, George Kaimakamis, Christos Konaxis, Gang Xu, Bulent Karakas, Aysel Turgut Vanli, Nurettin Cenk Turgay, Omer Kisi, Masashi Yasumoto, and Bendehiba Senoussi.
My academic ancestry includes the distinguished figures: Yusuf Yayli, H. Hilmi Hacisalihoglu, Esat Egesoy, Orhan Hamdi Alisbah, Ludwig Bieberbach, C. Felix Klein, Julius Plücker, Christian Ludwig Gerling, Johann Carl Friedrich Gauss, and Johann Friedrich Pfaff. Following C. Felix Klein, my intellectual lineage extends to Rudolf Otto Sigismund Lipschitz, Gustav Peter Lejeune Dirichlet, Simeon Denis Poisson, Jean-Baptiste Joseph Fourier, Joseph Louis Lagrange, and Leonhard Euler. This lineage traces back to Ibn Sina (Avicenna). See GEOMETREE .
Ph.D. in Mathematics, Ankara University, 2010, Thesis: Time-like Helicoidal and Rotational Surfaces with Light-like Profile Curve in Three-Dimensional Minkowski Space
Master's in Mathematics, Gazi University, 2005, Thesis: Helicoidal Surfaces in Three-Dimensional Minkowski Space
Bachelor's in Mathematics, Ondokuz Mayıs University, 1997
Calculus III (in English) Chapter 9, Chapter 10, Chapter 11, Chapter 12, Chapter 13
I wrote the following notes when I was an undergraduate student:
Diferensiyel Geometri (in Turkish) Differential Geometry
Doğrusal Cebir (in Turkish) Linear Algebra
Soyut Matematik (in Turkish) Abstract Mathematics
Soyut Cebir (in Turkish) Abstract Algebra
Topoloji (in Turkish) Topology
Diferensiyel Denklemler (in Turkish) Differential Equations
Analitik Geometri (in Turkish) Analytic Geometry
Sayılar Teorisi (in Turkish) Number Theory
Ölçüm Kuramı ve Fonksiyonel Analiz (in Turkish) Measure Theory and Functional Analysis
Kompleks Fonksiyonlar Teorisi (in Turkish) Theory of Complex Functions
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