Nicolas Libedinsky
Santiago, Chile
Soergel bimodules: representations, combinatorics and knots.
Abstract: We will start by defining the Hecke algebra of a Coxeter system and all the beautiful combinatorics attached to them appearing in the work of Kazhdan and Lusztig. We will see how some traces in this algebras link (via braid groups) this algebraic theory with the topological one of knots. Then we will "categorify" all of this constructions. This means roughly that we define categories that are very similar to these algebras or groups. In these categorifications Soergel bimodules are the fundamental objects and we will explain how they relate to combinatorics (explaining deep positivity phenomenons proved recently) and with the representation theory of algebraic groups, where they play a crucial role.