David Kazhdan

Abstract:   One of difficulties in the theory of harmonic analysis on reductive groups $G$ over local and global fields $F$ is the existence of elements $g',g'' \in G(F)$ which are conjugate over the algebraic closure $\bar F$ of $F$ but are not conjugate over $F$. The fundamental lemma shows that this failure can be corrected if one takes into account the existence of endoscopic groups. The fundamental lemma was recently proved by Ngo. I'll discuss the precise formulation and some applications of this result.