Title: Unifying definitions of analytic approximation and rigidity properties for discrete groups, quantum groups, and unitary tensor categories
Speaker: David Penneys (Ohio State University)
Abstract: Unitary tensor categories are mathematical objects which simultaneously generalize discrete groups and their categories of finite dimensional Hilbert space representations. They arise naturally in the context of quantum mathematical objects like von Neumann algebras and topologically ordered phases of matter. In this talk, we will discuss analytic approximation and rigidity properties for unitary tensor categories, like amenability, the Haagerup property, and Kazhdan's property (T), and how our definitions give a simultaneous definition for discrete groups and quantum groups as well. We will assume no familiarity with unitary tensor categories.