Research at Bilkent Mathematics

Research activities at the Department of Mathematics are grouped into four classical areas of pure and applied mathematics. Each group consist of several faculty members and graduate students and holds regular weekly seminars and other activities.

Algebra & Arithmetic

Commutative algebra, invariant theory, algebraic geometry, geometric group theory. Analytic number theory. Algebraic topology. Finite group theory, fusion systems. Representation theory, Clifford theory, G-algebras. Algebraic combinatorics, graph theory, G-posets. Ring theory. Formal concept analysis.

Participating faculty: Laurence J. Barker, Ahmet Güloğlu, Tomos Parry, Müfit Sezer, Özgün Ünlü, Hamza Yeşilyurt, Deniz Yılmaz

Analysis

Functional analysis, operator theory, operator algebras, matrix and numerical analysis, quantum operations. Potential theory, orthogonal polynomials, approximation theory. Complex analysis and operator theory in spaces of holomorphic and harmonic functions of several variables. Theory of entire functions, Polya frequency sequences. Analysis on Wiener space, Malliavin calculus and its applications, Monge-Kantorovich measure transportation and Monge-Ampere equation on Wiener space. Differential operators and differential equations. Dynamical systems, partial differential equations, delay differential equations.

Participating faculty: Fatihcan Atay, Alexander Goncharov, H. Turgay Kaptanoğlu, Konstantinos Maronikolakis, Türker Özsarı, Gökhan Yıldırım, Natalya Zheltukhina

Geometry & Topology

Algebraic geometry; geometry and arithmetic of K3-surfaces. Topology of real and complex algebraic varieties. Algebraic and geometric topology; classical knot theory. Geometric group theory, finite group actions on topological spaces, geometric structures associated to groups. Differential geometry, Riemannian geometry, pseudo-Riemannian geometry and Lorentzian geometry, global analysis on manifolds, general relativity and quantum field theories.

Participating faculty: Cihan Bahran, Kadri İlker Berktav, Alexander Degtyarev, Cihan Okay, Ali Sinan Sertöz, Bülent Ünal, Özgün Ünlü, Ergün Yalçın

Applied Mathematics

General relativity, mathematical physics; integrability of nonlinear PDEs, higher-dimensional classical field theories, strings and classical theory of gravitation. Mathematical theory of statistical physics, probability theory, financial mathematics, data science. Dynamical systems. Complex systems and network analysis. Systems and control theory. Mathematical biology and neuroscience.

Participating faculty: Fatihcan Atay, Metin Gürses, Yaghoub Heydarzade, Azer Kerimov, Naci Saldı, Gökhan Yıldırım

Theses archive

Department of Mathematics
Bilkent University
06800 Ankara, Turkey
Phone: +90 (312) 290-1586 / 266-4377
Fax: +90 (312) 266-4579