Department of Mathematics

Colloquium

  •  Daxin Xu, California Institute of Technology
  •  Exponential sums, differential equations and geometric Langlands correspondence
  •  01/09/2020
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall

The understanding of various exponential sums plays a central role in the study of number theory. 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, Heinloth-Ngô-Yun. In the end, 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.

 

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Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

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