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GRASP seminar
GRASP seminar
From relative Langlands to relative affine Springer fibers and Hitchin fibers
From relative Langlands to relative affine Springer fibers and Hitchin fibers
Organizers
Pengfei Huang
,
Tao Su
, Hao Sun
,
Mengxue Yang
Speaker
Zhiyu Zhang
Time
Wednesday, November 25, 2026 3:30 PM - 5:00 PM
Venue
A7-101
Online
Zoom 230 432 7880
(BIMSA)
Abstract
Group theory has played important roles in understanding geometric objects. For arithmetic applications, the absolute study of groups and the relative study of group actions are both fundamental. For each reasonable group action, we are led to consider cohomology of relative Hitchin fibers and affine Springer fibers, based on a GIT classification of orbits. In this talk, I will discuss some classical examples, such as the Jacquet-Rallis case from the action of GL_n on the standard representation and itself by conjugacy. I will discuss classification of orbits, computations of simple orbits, and the perverse-sheaf method to reduce the study of general orbits to simple orbits for certain questions. In particular, I will discuss joint work with Griffin Wang on the monoid version and proof of relative fundamental lemma for spherical Hecke modules, in the Jacquet-Rallis case.