Monday, February 7, 2022
Time | Items |
---|---|
All day |
|
4:00pm |
Hecke operators over local fields and an analytic approach to the geometric Langlands correspondence
02/07/2022 - 4:30pm Abstract: I will review an analytic approach to the geometric Langlands correspondence, following my work with E. Frenkel and D. Kazhdan, I will first discuss the simplest non-trivial example of Hecke operators over local fields, namely G=PGL(2) and genus 0 curve with 4 parabolic points. In this case the moduli space of semistable bundles Bun_G^{ss} is P^1, and the situation is relatively well understood; over C it is the theory of single-valued eigenfunctions of the Lame operator with coupling parameter -1/2 (previously studied by Beukers and later in a more functional-analytic sense in our work with Frenkel and Kazhdan). I will consider the corresponding spectral theory and then explain its generalization to N>4 points and conjecturally to higher genus curves. Location:
Zoom
|