Title: "Topological Matter, Anyons, and Categories"
Abstract: This talk is an introduction to topological phases of matter and category theory, the branch of mathematics behind them. The interplay between these two subjects is very rich and developments in each have led directly to developments in the other. We will introduce what a topological phase is, anyons, the important physical phenomenon they realize, and how to construct Hamiltonian models for both. At the heart of all of this are mathematical objects called fusion categories, the data for which are directly used in these constructions. The classification of fusion categories and their related structures is a classification of various models related to topological matter. We will discuss how this data is obtained and how, given this data, one can distinguish different Hamiltonians.
*Refreshments will be served before the colloquium*