By Viatcheslav Kharlamov
By Michele Ancona
By Olivier Benoist
By Bao Chau Ngo
Appears in collection : Summer School on the Langlands Program
The goal of these lectures is to sketch a general framework to study orbital integrals over equal characteristic local fields by means of moduli spaces of Hitchin type following the main lines of the proof of the fundamental lemma for Lie algebras. After recalling basic elements of the proof of the fundamental lemma for Lie algebras as well as recent related developments, I will explain an invariant theoretic construction which should a basic tool to understand general orbital integrals.