Exponential sums, differential equations and geometric Langlands correspondence

• 主讲人：Daxin Xu (AMSS CAS)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2023-04-13 20:00 - 2023-04-13 21:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/D13210BBC42F4A64DA49AA34E4227E7E
Valid Until: 2027-05-31 23:59

 

Abstract: In 1970s, Dwork established a relationship between the Bessel differential equation and the Kloosterman sums. Such a relationship can be regarded as an instance of the geometric Langlands correspondence for GL_2. In this talk, we will first review some classical results on exponential sums and differential equations, and then discuss some recent progress on generalizations of Dwork's result from the perspective of geometric Langlands correspondence. It is based on joint works with Xinwen Zhu and Kamgarpour-Yi.

 

Bio: Daxin Xu is an associated professor at the Institute of Mathematics, Academy of Mathematics and Systems Science, CAS. His research interests lie in arithmetic geometry, in particular, p-adic Hodge theory and geometric Langlands program. He received his Bachelor's Degree from Peking University in 2013, and his Ph.D. from Université Paris-Saclay in 2017.