EVENT DETAILS AND ABSTRACT

Title: The Space of Fusion Categories
Speaker: Noah Snyder
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Abstract:

Fusion categories are quantum analogues of finite groups. They play key roles in the study of topological quantum field theory, von Neumann subfactors, and condensed matter physics. There's a topological space (more precisely a homotopy 3-type) whose points are fusion categories. The goal of this talk is to explain what this space is and why it's interesting. In particular I'll touch on Etingof-Nikshych-Ostrik's classification of G-extensions of fusion categories, joint work with Pinhas Grossman describing certain connected components coming from exceptional subfactors, joint work in progress with Chris Douglas and Chris Schommer-Pries giving an explicit construction of an O(3) action on this space, and joint work with Grossman and David Jordan on a fibration of closely related spaces. Rather than dealing with any of these in depth, the emphasis of the talk will be on the big picture that a good way to study fusion categories is to look at the space of all of them.