## University of Sydney Algebra Seminar

# Ulrich Thiel (University of Sydney)

## Friday 31 March, 12-13pm, Place: Carslaw 375

## Introduction to the Calogero-Moser vs. Kazhdan-Lusztig program.

Long ago, it was discovered that Hecke algebras are an important tool in the representation theory of finite groups of Lie type. There are many invariants, like Lusztig families and Kazhdan-Lusztig cells, which can be defined using Hecke algebras and which help to bring some order to the representation theory. In the last decade it turned out that some of these invariants are also inherent to the representation theory of rational Cherednik algebras and the geometry of Calogero-Moser spaces. There are now several results and conjectures about this correspondence, a real understanding is missing so far, however. In my talk I will give a short overview about this, mainly focusing on one of the protagonists in the theory, the restricted rational Cherednik algebra.