## University of Sydney Algebra Seminar

# Geordie Williamson (University of Oxford)

## Friday 27 May, 2:30-3.30pm, Carslaw 175

### Coxeter groups, Soergel bimodules and higher representation theory

Many important representation theoretic objects (for example Hecke algebras and enveloping algebras) can be categorified. Over the last decade important new results in representation theory have been obtained by studying actions of these categorifications.

In my talk I will try to explain this in a simple example: that of actions of Coxeter groups on categories. Even this naive example is somewhat subtle, and one is led naturally to certain generalisations of the Zamolodchikov equations arising from the Platonic solids. I will explain how this leads to a generators and relations description of the monoidal category of Soergel bimodules. This answers a question of Rouquier and formed the starting point of this work. (Joint work with Ben Elias.)