Representation theory is a branch of modern mathematics that studies realizations of abstract structures via ``classical'' concrete structures. It is an active and dynamic area with connections, in particular, to algebra, combinatorics, geometry, topology, analysis, category theory, number theory and mathematical physics. The aim of the present program is to further investigate and develop both the representation theory and its connections via detailed study of various types of representations addressing problems of classification, description, construction and realization of representations, study of their invariants and applications.
The main emphasis of the program will be on:
- categorification and higher representation theory, homological algebra
- cluster algebras; - representation theory of algebraic groups
- representation theory of associative algebras
- representation theory of Lie (super)algebras and quantum (super)groups.