Representation theory is a fascinating mathematical subject that studies symmetries in vector spaces. It has connections with many other areas such as algebraic combinatorics, algebraic geometry, number theory, mathematical physics, and computer science, just to name a few.
Some of the specific lines of research in representation theory and related areas pursued by our faculty are described below.
- Representations of Finite Dimensional Algebras and Invariant Theory - Calin Chindris
Dr. Chindris' research interests are at the intersection of representation theory of finite dimensional algebras and invariant theory. This approach to representation theory enables one to study/parametrize large families of representations via moduli spaces for finite dimensional algebras and other invariant theoretic objects. It also leads to applications to algebraic combinatorics such as the study of LittlewoodRichardson coefficients and cluster fans.
- Representations of p-adic groups and automorphic representations - Shuichiro Takeda
Dr. Takeda's research focuses on representation theory of reductive groups over p-adic fields and automorphic representation theory, both of which are usually in infinite dimensional complex vector spaces. Those representations are the main objects of study in the Langland’s program.