Fusion Categories, Hyperplane Complements and The K(π, 1) Conjecture
June 9, 2025 (Monday), 3:30 pm – 4:30 pm A4#G06
Edmund Heng
Postdoctoral fellow
University of Sydney
Research interests: Representation theory, category theory, topology and dynamics. Specifically, Categorification, Coxeter and Artin–Tits groups, quivers and algebras, tensor and fusion categories, and beyond.
Speaker Introduction
Dr. Edmund Heng is currently a postdoctoral fellow at the University of Sydney, working under Oded Yacobi and Geordie Williamson. From 2022-2025 Dr. Edmund Heng was a postdoctoral fellow at the Institut des Hautes Études Scientifiques IHÉS. He completed his PhD in 2022 at the Australian National University, under the supervision of Anthony Licata.
Abstract
There is a numerical coincidence between fusion categories (or fusion rings) and Coxeter theory - the numbers 2cos(π/m) show up in both of them. In this talk, I would like to convince you that this is more than just a naive observation, and can be used as a catalyst to generalize 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(π, 1) conjecture, which involve hyperplane complements associated to Coxeter groups and their universal covers.