Julia Plavnik (Bloomington, IN)
Abstract
Modular categories arise naturally in many areas of mathematics, such as conformal field theory, representations of braid groups, quantum groups, and Hopf algebras, low dimensional topology, and they have important applications in condensed matter physics.
Despite recent progress on the classification of modular categories, we are still in the early stages of this theory and the general landscape remains largely unexplored. One important step towards deepening our understanding of modular categories is to have well-studied constructions. In this talk, we will present an overview of various of these constructions and compare their properties. We will focus on symmetry gauging, ribbon zesting, and the relative Deligne tensor product.