The current interests concentrate in mainly two areas; analysis and its applications (applied functional analysis, differential equations, numerical analysis), algebra and number theory and their applications (in particular, modular forms, finite fields, coding theory, and cryptography).
Sabancı University has graduate programs leading to M.Sc and Ph.D degrees in Mathematics and a Minor Honors Program in Mathematics aimed at students of engineering and economics programs. The research within the Mathematics Group at Sabancı University focus on:
- Algebra, Number Theory and Applications (finite fields, curves over finite fields, algebraic coding theory, pseudorandom number generators, enumerative combinatorics, integer partitions and q-series).
- Analysis (functional and complex analysis, differential equations, probability and distributions).
Algebra and Number Theory
The theory of finite fields has a long tradition in mathematics. Originating from problems in number theory (Euler, Gauss), the theory was first developed purely out of mathematical curiosity. For a long time, this theory was used exclusively in pure mathematics, in areas such as number theory, algebraic geometry, group theory, and so on, without any relevance to applications. The situation changed dramatically with the development of modern information technologies. Finite fields were recognized to provide a natural framework for a wide variety of applications, particularly in information transmission and data security.
The research areas of the Number Theory/Algebra Group at Sabancı University include several aspects of the theory of finite fields, in particular, curves over finite fields and their applications to coding theory, the generation and analysis of pseudorandom numbers, as well as integer partitions and q-series.
There has been tremendous research activity in the last decades focusing on curves over finite fields, or equivalently algebraic function fields over finite fields. Interesting results were obtained, such as the construction (by A. Garcia and H. Stichtenoth) of explicit towers of function fields meeting the Drinfeld-Vladut bound.
The active, international collaboration of the Number Theory/Algebra Group is reflected by recent events such as "September Research on Curves over Finite Fields", the "SU Lecture Series on Coding Theory" and "Semester on Curves, Codes and Cryptography".
The research interests of the Analysis Group lie mainly in Functional Analysis and Complex Analysis with emphasis on the structure theory of locally convex spaces; in particular, spaces of analytic, harmonic, and infinitely differentiable functions of several variables.
The following areas are of particular interest: linear topological invariants, isomorphisms and bases in locally convex spaces; complex potential theory, approximation and interpolation of analytic and harmonic functions, composition operators on analytic function spaces; probability measures in infinite dimensional spaces, nonlinear theory of distributions; as well as operator theory, pseudo-differential operators and partial differential equations. In this mathematical landscape, geometry, functional analysis, complex and real analysis work together to create a rich set of phenomena, many of which still have to be understood.
The Analysis Group initiated the Istanbul Analysis Seminars, which takes place every Friday. Furthermore, the Group is part of an international network for Functional and Complex Analysis comprising other groups from Wuppertal, Trier, Valencia, Ann Arbor, Poznan, Duesseldorf, Krakow, Rostov-on-Don, Uppsala, Tel Aviv, Toulouse. In the frame of this network, the conference on Real Analytic and Complex Analytic Methods in Functional Analysis was hosted by Sabancı University (September 20-24, 2004). This Conference was preceded by three others, Linear Topological Spaces and Complex Analysis (Edirne, 1994, 1996, 1999), as well as the summer semester in Complex Potential Theory (Feza Gursey Institute, 1999).
Additionally, some Group members also take part in the Istanbul Seminars in Partial Differential Equations and Applications, as well as in related projects involving several Istanbul universities.
This school offers programs in: