# Asymptotic Hecke ring of a Weyl group

SPEAKER: Victor Ostrik

TITLE: Asymptotic Hecke ring of a Weyl group

ABSTRACT This is a joint work with R.Bezrukavnikov and M.Finkelberg. Asymptotic Hecke ring of a Weyl group was defined by Lusztig. One can think informally that this ring is a limit of usual Hecke algebra as the parameter tends to infinity. Lusztig gave precise conjecture describing the structure constants of this ring with respect to its canonical basis. We will explain a proof of this conjecture. A categorification of this conjecture (also due to Lusztig) plays a crucial role in this proof.