George Altmann (University of Leeds) – Braid Groups and Their Representations

The (Artin) braid group is an important and well-studied group with applications in algebra, geometry, and mathematical physics. I will introduce some of the ways the braid group presents itself and discuss two well-known representations coming from topology: the Artin representation and the Burau representation. These representations will help to demonstrate the connection between braids and knots. I will then go on to introduce a natural generalisation of the braid group, called the loop braid group, and discuss how the Artin and Burau representations lift for this group.