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: 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.
March 3, 2025
Speaker: Dennis Hou
Title: pre Tannakian categories
Apr. 7, 2025
Speaker: Nick Backes
Title: Supercuspidal Representations, part 2+
Abstract: I have given a lot of GARTS talks on supercuspidals, but some people wanted to know more, so I will give yet another talk on supercuspidals. This talk will not require knowledge from previous talks. This talk will focus on various characterizations of supercuspidals
Apr. 14, 2025
Speaker: Trisha Kothavale
Title: Hopf Algebras and Diagrammatic Calculus
Abstract: Braided tensor categories generalize ideas of symmetry and commutativity to category theory. To study braided categories, it makes sense to look at Hopf algebras and their Yetter-Drinfeld modules. I will define Hopf algebras and connect them to quantum groups. I will also define a diagrammatic algebra that can be used in tensor categories that lends itself to constructing knot invariants.
Fall 2022 Talks (Songhao)
Spring 2021 Talks (Jason Saied)