During the Winter 2026 quarter, all of our meetings will be held in-person in 268 Skye Hall. This quarter, we'll have mostly-local speakers giving mostly-expositional talks close to the theme of "representation theory and character varieties."
Talks will run from 12:30-1:30pm unless otherwise indicated, but feel free to show up early for socializing with the speaker.
Current organizers: Peter Samuelson
Winter 2026 schedule
January 8, 2026
Organizational Meeting
Jaunary 15, 2026
Peter Samuelson (UCR)
Title: Introduction to skein theory and character varieties
January 22, 2026
Brian Collier (UCR)
Title: Introduction to Higgs bundles and the non-abelian Hodge correspondence
January 29, 2026
Tom Gannon (UCR)
Title: K-theory and the affine Grassmannian
February 5, 2026
Tom Gannon (UCR)
Title: Coulomb branches and their quantizations
February 12, 2026
Peter Samuelson (UCR)
Title: "Skein algebras and quantized Coulomb branches" by Allegretti and Shan
February 19, 2026
Chris Grossack (UCR)
Title: Character varieties from factorization homology
February 26, 2026
Pallav Goyal (UCR)
Title: The commuting scheme of Lie algebras
March 5, 2026
Elad Zelingher (University of Michigan)
Title: Special values of Bessel functions for representations of finite general linear groups
Abstract: The Whittaker model is an important concept in representation theory of reductive groups and the Langlands program. It is a source for interesting irreducible representations called generic representations. Given an irreducible generic representation of a finite group of Lie type G one can attach a special matrix coefficient to it called the normalized Bessel (or bi-Whittaker) function. Determination of explicit values of Bessel functions has been a long lasting problem. In this talk I will present my results regarding computation of special values of Bessel functions of different sorts for finite general linear groups through the mechanism of gamma factors. I will also talk about the relation to Katz's exotic Kloosterman sums and sheaves and about my upcoming work with Robert Cass and Pam Gu extending this sort of relation to the Kloosterman sheaf of Heinloth--Ngô--Yun for generic principal series representations of more general finite connected reductive groups.
March 12, 2026
Thomas Hameister (Boston College)
Title: Relative Hitchin Systems and Endoscopy
Abstract: The endoscopic Fundamental Lemma is a formula computing certain orbital integrals for a group G in terms of orbital integrals for related endoscopic groups. While Langlands first believed that this formula should be a quick calculation taking no more than a few weeks to solve, a remarkable amount of geometry has arisen from this equation, culminating in Ngo Bao Chau's proof of the Fundamental Lemma almost 30 years later. S. Leslie more recently proposed endoscopic fundamental lemmas associated to symmetric varieties X=G/H instead of to a reductive group G. In this talk, I will discuss the geometric spaces and techniques that go into a proof of a special case of these new fundamental lemmas. In particular, I will introduce Higgs bundles and affine Springer fibers for symmetric varieties, and will discuss how the local and global pictures interact. If time permits, I will remark on some connections to the relative Langlands program, including a remarkable connection between the invariant theory of spherical varieties and an associated symplectic representation of the dual group G_X^\vee. This is based on joint work with Spencer Leslie.