Fusion rings and their categorifications

Speaker: Andrew Schopieray

Date: 2021

Location: Zoom, PIMS, University of Alberta

Conference: Emergent Research: The PIMS Postdoctoral Fellow Seminar

Subject: Mathematics

Class: Scientific

Abstract:

Fusion rings are a special class of associative unital rings with nonnegative integer structure constants and a notion of duality. For example, the group ring of a finite group is a fusion ring. We study fusion rings mainly because they arise as Grothendieck rings of categories associated to Hopf algebras, semisimple Lie algebras, vertex operator algebras, etc. In turn, these categories have application to topological quantum field theory, invariants of knots and links, and quantum computation, to name a few. In this talk we will discuss the brief history of the classification of categorifiable fusion rings and how number-theoretic properties of fusion rings dictate the existence of, or properties of, their categorifications.