Title: Gauging the symmetry of modular categories
Speaker: Julia Plavnik (Texas A&M University)
Abstract: Modular categories are interesting algebraic structures connected with a variety of mathematical subjects including topological quantum field theory, conformal field theory, representation theory of quantum groups, von Neumann algebras, and vertex operator algebras. In addition to the mathematical interest, a motivation for pursuing a classification of modular categories comes from their application in condensed matter physics and quantum computing. Gauging is a well-known theoretical tool used in physics to promote a global symmetry to a local gauge symmetry. This is an useful tool to construct new modular categories from given ones.
In this talk, we will start by introducing some of the basic definitions and properties of modular categories, and we will also give some basic examples to have a better understanding of their structures. We will also present a mathematical formulation of gauging in terms of higher category formalism. We will show through concrete examples which are the ingredients involved in this process. In addition, if time allows, we will mention some classification results and open problems related with gauging.
Seminar URL: http://yutsumura.com/quantum-algebra-topology-seminar/
