 
Summary: Proceedings of the International Congress of Mathematicians
Hyderabad, India, 2010
The Work of Ng^o Bao Ch^au
James Arthur
Abstract
Ng^o Bao Ch^au has been awarded a Fields Medal for his proof of the fundamental
lemma. I shall try to describe the role of the fundamental lemma in the theory
of automorphic forms. I hope that this will make it clear why the result will be
a cornerstone of the subject. I will also try to give some sense of Ng^o's proof.
It is a profound and beautiful argument, built on insights mathematicians have
contributed for over thirty years.
Mathematics Subject Classification (2000). Primary 11F55; Secondary 14D23.
Keywords. Fundamental lemma, trace formula, Hitchin fibration, affine Springer
fibres, stabilization.
The Formal Statement
Here is the statement of Ng^o's primary theorem. It is taken from the beginning
of the introduction of his paper [N2].
ThŽeor`eme 1. Soient k un corps fini `a q ŽelŽements, O un anneau de valuation
discr`ete complet de corps rŽesiduel k et F son corps des fractions. Soit G un
schŽema en groupes rŽeductifs audessus de O dont le nombre de Coxeter multipliŽe
