  This article is a Bourbaki seminar report on Ngo Bao Chau's proof of the
fundamental lemma. About thirty years ago, R. P. Langlands conjectured a
collection of identities to hold among integrals over conjugacy classes in
reductive groups. Ngo Bao Chau has proved these identities (collectively called
the fundamental lemma) by interpreting the integrals in terms of the cohomology
of the fibers of the Hitchin fibration. The fundamental lemma has profound
consequences for the theory of automorphic representations. Significant recent
theorems in number theory use the fundamental lemma as an ingredient in their
proofs.
