Characters of finite Chevalley groups and categorification
Representation theory of finite groups seeks to understand functions on the group known as irreducible characters. A group like GL(n,F_q), the group of invertible square matrices with entries in a finite field F_q, originates in algebraic geometry, thus its irreducible characters should also be understood via algebraic geometry. A magnificent realization of that idea is provided by the theory of character sheaves created by Lusztig in 1980's. I will explain how a systematic use of categorification allows to make some results of this theory including classification of character sheaves more transparent. The talk is based on a joint with with M. Finkelberg and V. Ostrik and a work in progress with D. Kazhdan and Y. Varshavsky.