My main area of research is geometric representation theory (with applications to algebraic geometry, number theory and mathematical physics). Currently I am working on two main subjects: the first (jointly with M.Finkelberg and H.Nakajima) is an attempt to give a mathematically rigorous approach to the study of 3-dimensional N=4 super-symmetric gauge theories and their quantizations and study representations of the resulting non-commutative algebras.
The 2nd subject has to do with representation theory of p-adic groups (in particular, p-adic interpretation of Lusztig's asymptotic Hecke algebra and its generalizations).