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, Matthew Gelvin, Ahmet Güloğlu, Anargyros Katsampekis, Alexander Klyachko, Yosum Kurtulmaz, Müfit Sezer, Özgün Ünlü, Hamza Yeşilyurt

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, delay differential equations.

Participating faculty: Fatihcan Atay, Aurelian Gheondea, Alexander Goncharov, H. Turgay Kaptanoğlu, Mefharet Kocatepe, Ali Süleyman Üstünel, 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: Alexander Degtyarev, Matthew Gelvin, Alexander Klyachko, 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. Dynamical systems. Complex systems and network analysis. Systems and control theory. Mathematical neuroscience.

Participating faculty: Fatihcan Atay, Metin Gürses, Azer Kerimov, Ali Süleyman Üstünel
Department of Mathematics
Bilkent University
06800 Ankara, Turkey
Phone: +90 (312) 290-1586 / 266-4377
Fax: +90 (312) 266-4579