Abstract:

In this short course, we give an introduction to the geometry of Hitchin fibration and its application to local orbital integrals. We will explain the work of B.C. Ngo that relates the Langlands-Shelstad fundamental lemma and nonstandard fundamental lemma for Lie algebras to an identity about point counting of Hitchin fibers, then we will explain a recent alternative proof of the latter by Groechenig-Wyss-Ziegler that uses p-adic integration and Langlands duality for Hitchin fibers.

Topics include:

1. Geometry of Hitchin fibration
2. Langlands duality of Hitchin fibers
3. Local Tate duality for abelian varieties and p-adic integration
4. Relation with fundamental lemma

Reference:

T. Chen and X. Zhu, Geometric Langlands in prime characteristic, Compositio 2017
M. Groechenig, D. Wyss, P. Ziegler, Geometric stabilisation via p-adic integration, JAMS 2020
Ngo, Le lemme fondamental pour les algebres de Lie, Publications mathematiques de I'IHES, 2010

Time:

4/6      13:00-14:30, 15:30-17:00

4/13    13:00-14:30, 15:30-17:00

4/20    13:00-14:30, 15:30-17:00

4/27    13:00-14:30, 15:30-17:00