Geordie Williamson

Abstract:   It is a surprising fact that many mathematical structures can be categorified. Objects that we have spent decades thinking about as sets are actually the Grothendieck groups of categories. I will discuss an interesting example of this phenomenon, provided by the Hecke algebra of a reflection group. Hecke algebras possess a remarkable basis discovered by Kazhdan and Lusztig. This basis admits an elementary inductive definition, but establishing even its most basic properties has, up until now, required the use of deep tools from algebraic geometry. I will explain how ideas from categorification and Hodge theory shed new light on this basis. This is joint work with Ben Elias.