Feb. 17, 2025
Speaker: Dan Tan
Title: From groups to tensor categories and back
Abstract: The finite-dimensional representations of a finite group form a category. However, two non-isomorphic groups can produce equivalent categories (even up to equivalence of linearly enriched categories). The tensor product of representations gives more context to distinguish these categories. In this talk, we will explain how to reconstruct a finite group from its tensor category of finite-dimensional representations by looking at the automorphisms of its fibre functor.
Feb. 24, 2025
Speaker: Dr. Forrest Thurman
Title: Overview of Representation Theory of Compact Groups
Abstract: T I will give an overview of the some of the more important theoretical results for the representation theory of compact groups, which can be seen as a generalization of the rep theory of finite groups. Just as in the case of finite groups, every irreducible representation is finite dimensional and contained in the regular representation. However, for non-finite compact groups, there are infinitely many irreducible representations. We will sketch the proof of existence and uniqueness of Haar measure on a compact group, and discuss character theory in the setting of connected Lie groups with SU(2) as the main example. Time permitting, we will also cover the Hopf algebra of representative functions on G, and see how Tannaka-Krein duality implies compact groups are actually real algebraic groups.
Fall 2022 Talks (Songhao)
Spring 2021 Talks (Jason Saied)