Tue, January 20, 2026
1:50 pm - 2:45 pm
Math Tower (MW) 154
Sean Sanford
University of Edinburgh
Title
Obscure Galois Theory and an Invertibility Criterion
Abstract
In 2003, Kuperberg published a paper with the baffling title "Finite, connected, semisimple, rigid tensor categories are linear". His result produces a particular field from a curious Galois theory scenario that arises when considering 2-categories. If we think of a fusion category as a 2-category with one object, it turns out that Kuperberg's field is precisely the endomorphisms of the unit inside of the Drinfeld center.
In this talk we will discuss Kuperberg's techniques, and how they lead to a new invertibility criterion. We will then show how this easy to check condition leads to many useful results in the theory of separable fusion categories over arbitrary fields.