Bessel equations, hypergeometric sums and geometric Langlands correspondence
ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR
Date
Thursday, April 28, 2022 13:00 - 15:00
Speaker
Daxin Xu (Morningside Center of Mathematics)
Location
https://mathseminars.org/seminar/AGNTISTA
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
Tamas Hausel
Contact
I will first review the relationship between the Kloosterman sums and the classical Bessel differential equation. Recently, there are two generalizations of this story (corresponding to GL_2-case) for arbitrary reductive groups using ideas from the geometric Langlands program, due to Frenkel-Gross and Heinloth-Ngô-Yun. I will discuss my joint work with Xinwen Zhu where we unify previous two constructions from the p-adic aspect and identify the exponential sums associated to different groups as conjectured by Heinloth-Ngô-Yun. I will also talk about my recent joint work with Masoud Kamgarpour and Lingfei Yi on the generalization of the above story to hypergeometric sheaves.