Speaker
Maarten Solleveld
Description
Graded Hecke algebras can arise in several ways. On the one hand they describe categories of representations of reductive $p$-adic groups. On the other hand they admit a geometric construction, in terms of equivariant constructible sheaves on complex algebraic varieties. We will discuss how this can be applied to solve some problems in the representation theory of $p$-adic groups. We will focus on the $p$-adic Kazhdan-Lusztig conjecture, which expresses the multiplicity of an irreducible representation in a standard module as the multiplicity of a local system in a perverse sheaf.