**Beijing Algebraic Geometry Colloquium**10th Meeting

September 29, 2018

Room A304, Dept. of Math, Tsinghua

**Algebraic Geometry Activities in China**Ahmed Abbes

(CNRS & IHES)

The p-adic Simpson correspondence

14:00 - 15:00

The p-adic Simpson correspondence, initiated by Gerd Faltings in 2005, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra - namely Higgs bundles. My lecture will be an introduction to this topic. I will focus on the approach that I developed with Michel Gros relying on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J.-M. Fontaine.

Daxin Xu 许大昕

(Caltech)

Generalized Kloosterman sheaves and their p-adic variants

15:30 - 16:30

I will first review the relationship between the classical Bessel equation and the classical Kloosterman sum. Such a relation can be regarded as an instance of the geometric Langlands correspondence for GL2. I will then explain the recent generalizations of this story for arbitrary reductive groups, based on the works by Frenkel-Gross, Heinloth-Ngo-Yun, and X. Zhu. In the end, I will discuss some joint work in progress with X. Zhu, where we study the p-adic aspect of this theory.

**Organized by****Baohua Fu**CAS**Lei Fu**Tsinghua**Xiaotao Sun**CAS**Zhiyu Tian**PKU**Qizheng Yin**PKU**Past Meetings**

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AG Activities in China

Algebraic geometry activities in Beijing and throughout China.

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