Seminar
Representation theory seminar 2025 Semester 1
Organisers: Dougal Davis, Kari Vilonen, Ting Xue
Place and time: Peter Hall 162, 2-4PM
Please contact one of the organisers to be added to the mailing list.
Upcoming Talks
3 Apr Yau Wing Li (Melbourne) Endoscopy for metaplectic affine Hecke categories
Abstract: Lusztig (1994) studied sheaves on the enhanced affine flag variety with fixed monodromy along Kac-Moody torus orbits, developing a framework that later became central to the metaplectic and quantum geometric Langlands program. In joint work with Gurbir Dhillon, Zhiwei Yun, and Xinwen Zhu, we show that these monodromic affine Hecke categories are equivalent to non-monodromic affine Hecke categories of smaller groups, constructed via an affine analogue of Langlands’ endoscopy, extending results of Lusztig and Yun for finite Hecke categories. Applications include endoscopic equivalences, confirming a series conjectured by Gaitsgory in quantum geometric Langlands.
10 Apr Peter McNamara (Melbourne) The Spin Brauer Category
Abstract: The Brauer category is a tool that controls the representation theory of (special) orthogonal Lie groups and Lie algebras. A drawback is it doesn’t see the spin representations. We introduce and study a spin version, the Spin Brauer category, which sees the entire representation theory of type B/D Lie algebras. This is joint work with Alistair Savage.
Past Talks
31 Jan (Friday) 3-5pm: (Note unusual date and time!)
Oscar Kivinen (Aalto University) Shalika germs and localization on Hilbert schemes
Abstract: Shalika’s germ expansion allows us to understand regular semisimple orbital integrals for reductive Lie algebras over non-archimedean local fields in terms of nilpotent orbital integrals. In work with Tsai, we gave an algorithm to compute most orbital integrals and Shalika germs for 
6 Feb Jonathan Gruber (FAU Erlangen-Nürnberg) Tensor structures for affine Lie algebras at positive levels
Abstract: An affine Lie algebra g is a central extension of the loop algebra of a complex simple Lie algebra, and a g-module is said to have (relative) level k if the canonical central element acts by the scalar k-h, where h is the dual Coxeter number. For all levels k that are not positive rational or zero, Kazhdan and Lusztig have defined a braided monoidal structure on a parabolic BGG category O of g-modules of level k. In this talk, I will explain the definition of a braided monoidal structure on the category O at positive rational levels, via a monoidal enhancement of Brundan and Stroppel’s semi-inifnite Ringel duality.
This is based on joint work with Johannes Flake and Robert McRae.
13 Feb Peter Fiebig (FAU Erlangen-Nürnberg) 1:15pm (Note unusual time!)
A chromatic decomposition of the equivariant cohomology of Grassmannians
Abstract: In 2014 George Lusztig asked if there are “higher generations of quantum groups” that further extend the approximation of the representation theory of algebraic groups in positive characteristics by quantum groups at roots of unity. One approach towards an answer is to employ cohomology theories of higher chromatic height (quantum groups correspond in a precise way to height 1, the modular representation theory to height infinity). So far there is no definition of these higher generation quantum groups, yet I would like to report on recent progress towards a solution in type A1. This is joint work with Yaping Yang and Gufang Zhao.
20 Mar Jiuzu Hong (U North Carolina at Chapel Hill) Global Schubert varieties of parahoric Bruhat-Tits group schemes
Abstract: Global Schubert varieties of parahoric BT group schemes were introduced by Xinwen Zhu in his proof of the coherence conjecture of Pappas-Rapoport. These global Schubert varieties provide flat families relating spherical Schubert varieties in affine Grassmannians and other Schubert varieties or their unions in partial affine flag varieties. In this talk, I will talk about line bundles over global Schubert varieties and their equivariant structures, along with some applications. This talk will be based on the joint work with Huanhuan Yu.
27 Mar Jingren Chi (Morningside Center CAS) Cohomology of simple Shimura varieties for non qusi-split local groups
Abstract: The Langlands-Kottwitz method gives a recipe to describe the etale cohomology of Shimura varieties at a place of good reduction, as a bridge between representations of local Galois groups and Hecke algebras. Scholze generalizes their approach to many cases of bad reduction, allowing arbitrary deep level structure while assuming the relevant local group is still quasi-split. In this talk, we will review these stories and explain the new ingredients needed to treat the case where the local group is non quasi-split. This is based on joint work with Thomas Haines.