Braid groups, and some representations

Date: Tuesday 25 October 2022

Abstract

Braid groups occur in Lie theory, each naturally associated to a Coxeter group, and in topology, due to their close relationship with knots and knot invariants. In this talk I will first introduce braids algebraically, then talk about connections with topology - realising braid groups as fundamental groups or mapping class groups. I’ll then explain some of the open problems in the representation theory of braid groups, including the faithfulness of the Burau representation.