Character sheaves, categorification and Springer theory

A major achievement of representation theory of finite
Chevalley groups is the theory of character sheaves
created mostly by Lusztig in 1980’s. I will explain, based on a joint
work with Finkelberg and Ostrik, how a systematic application of the
categorification idea can lead to a drastic simplification of Lusztig’s
classification of character sheaves. Time permitting I will describe the
joint project with Kazhdan and Varshavsky where these constructions are
generalized to loop groups; these generalizations are closely related
to geometric Langlands duality, endoscopy theory in harmonic analysis
on p-adic groups and some recent works of G. Lusztig.