BIMSA > GRASP seminar A Deligne-Simpson problem for irregular G-connections over P^1
A Deligne-Simpson problem for irregular G-connections over P^1
Organizers
Pengfei Huang , Tao Su , Hao Sun
Speaker
Konstantin Jakob
Time
Wednesday, April 10, 2024 3:00 PM - 4:00 PM
Venue
A3-4-312
Online
Zoom 242 742 6089 (BIMSA)
Abstract
The Deligne-Simpson problem asks for the existence of meromorphic G-connections with prescribed local behavior at the poles. I will explain joint work with Zhiwei Yun in which we give a solution to this problem for G-connections on P^1 with two poles, one of which is regular singular with residue in a fixed nilpotent orbit, the other of which is irregular and satisfies a condition that we call isoclinic (all slopes are equal). Perhaps surprisingly, our solution is related to the representation theory of the rational Cherednik algebra. If time permits, I will discuss joint work with Andreas Hohl regarding uniqueness (rigidity) of the solution for two famous families of such G-connections, the Kloosterman (aka Frenkel-Gross) G-connection and the Airy G-connection. Our approach is based on the Stokes phenomenon for irregular connections.