Representations of Braid Groups and Motion Groups

Abstract: Representations of braid groups appear in many (related) guises, as sources of knot and link invariants, transfer matrices in statistical mechanics, quantum gates in topological quantum computers and commutativity morphisms in braided fusion categories. Regarded as trajectories of points in the plane, the natural generalization of braid groups are groups of motions of links in 3 manifolds. While much of the representation theory of braid groups and motions groups remains mysterious, we are starting to see hints that suggest a few conjectures. I will describe a few of these conjectures and some of the progress towards verification.

mathematical physicscategory theoryquantum algebrarepresentation theory

Audience: researchers in the topic

Online GAPT Seminar

Series comments: Description: Seminar of the GAPT group at Cardiff University