University of Sydney Algebra Seminar

Edmund Heng

Friday 2 May, 12-1pm, in Carslaw 175

Fusion categories and Coxeter theory

There is a numerical coincidence between fusion categories (or fusion rings) and Coxeter theory — the numbers \(2\cos(\pi/m)\) show up in both of them. In this talk, I’d like to convince you that this is more than just a naive observation, and can be used as a catalyst to generalise well-known relations between different mathematical objects (quivers, Lie algebras, cluster algebras etc.). More specifically, I will speak on applications of fusion categories to problems surrounding the \(K(\pi,1)\) conjecture, which involve hyperplane complements associated to Coxeter groups and their universal covers.