During the Fall 2025 quarter, all of our meetings will be held in-person in 268 Skye Hall.
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: Carl Mautner, Tom Gannon
Fall 2025 schedule
September 30, 2025
Sam Gunningham (Montana State University)
Title: Deformation Quantization and Perverse Sheaves
Abstract: Given a holomorphic symplectic manifold and a pair of oriented holomorphic lagrangian submanifolds, the lagrangian intersection carries a canonical perverse sheaf known as the DT sheaf. On the other hand, the theory of deformation quantization provides another, seemingly quite different, construction of a perverse sheaf. I will explain some recent results with Pavel Safronov in which we identify these two constructions, shedding new light on Joyce's conjectural description of the holomorphic Fukaya category. Time permitting, I will outline an application of these results, in which we related the skein module of a 3-manifold to the sheaf-theoretic Floer homology of Abouzaid and Manolescu.
October 7, 2025
Sam Qunell (UCLA)
Title: 2-categorical affine symmetries and q-boson algebras
Abstract: Representations of KLR (quiver Hecke) algebras categorify the positive part of the quantum group associated to any symmetrizable Cartan matrix. This categorical perspective makes certain symmetries more natural to study. For example, the induction and restriction functors between categories of KLR algebra modules play an important role in the theory. A closer investigation of these functors reveals surprising new symmetries. In this talk, I will explain how the induction and restriction functors for KLR algebras can be used to obtain a 2-representation of the corresponding affine positive part in type A. I will also describe a new categorification of a closely related algebra, the q-boson algebra, in all symmetrizable Kac-Moody types.
October 14, 2025
Pallav Goyal (UCR)
Title: Hall algebras and shifted quantum affine algebras
Abstract: In 2017, Finkelberg and Tsymbaliuk introduced the notion of shifted quantum affine algebras and described their role in the study of quantized Coulomb branches associated with certain 3D N = 4 quiver gauge theories. We describe a new geometrical construction of a deformation of one of these shifted quantum affine algebras as the Hall algebra of the category of restricted representations of the Lie algebra sl_2 over a finite field. The main tool we use is an equivalence of categories by Rudakov that relates the above category to that of representations over a certain quiver modulo relations. This is joint work with Peter Samuelson.
October 21, 2025
Kent Vashaw (UCLA)
Title: Support varieties and tensor-triangular geometry for Hopf algebras
Abstract: Support varieties, in many different forms, have been a major tool in representation theory, and include Quillen's cohomological support varieties for finite groups, Carlson's rank varieties for elementary abelian p-groups, Snashall--Solberg's Hochschild support varieties for finite-dimensional algebras, and the Pi-point supports of Friedlander--Pevtsova for finite group schemes. The Balmer spectrum is a formally defined space that provides a universal support for any tensor-triangulated category, and in many cases is homeomorphic to more concretely-defined support varieties. We will discuss a recent program for classifying the Balmer spectra and support varieties for finite-dimensional Hopf algebras, which will include joint work with Nakano—Yakimov, and Huang.
October 28, 2025
No Seminar
November 4, 2025
Chris Grossack (UCR)
Title: Local Relations in the Hall Algebra of a (Locally) Gentle Algebra
Abstract: The derived category of a (locally) gentle algebra admits a "geometric model" in the Fukaya category of an associated surface. This Fukaya category has (direct sums of) curves as objects and intersection points as arrows, making the classification of indecomposables pleasantly combinatorial. One can use this geometric model to compute the Hall algebra of the category (in either Toën's derived sense or in Gorsky's semi-derived sense), which gives a description of the Hall algebra in terms of local relations between curves in the surface. In this talk we'll primarily review the translation between representation theory and topology, based on work of Haiden--Katzarkov--Kontsevich, Opper--Plamondon--Schroll, and Lekili--Polischuk, and with any remaining time we'll describe the implications for Hall algebras.
November 11, 2025
Veterans Day Holiday (No Seminar)
November 18, 2025
Kendric Schefers (UC Berkeley)
Title: TBA
Abstract: TBA
November 25, 2025
Thanksgiving Holiday (No Seminar)
December 2, 2025
Robert Cass (Claremont McKenna College)
Title: TBA
Abstract: TBA