The Work of Ngo Bao Chau

TL;DR

Ngo Bao Chau's groundbreaking work connects the Hitchin fibration with the Arthur-Selberg trace formula, culminating in his proof of the Fundamental Lemma for Lie algebras, which earned him the Fields Medal.

Contribution

The paper introduces Ngo Bao Chau's innovative approach linking geometric and automorphic methods, notably his proof of the Fundamental Lemma for Lie algebras.

Findings

Proof of the Fundamental Lemma for Lie algebras

Connection between Hitchin fibration and trace formula

Recognition with Fields Medal

Abstract

In August 2010, Ngo Bao Chau was awarded a Fields Medal for his deep work relating the Hitchin fibration to the Arthur-Selberg trace formula, and in particular for his proof of the Fundamental Lemma for Lie algebras. This article gives a brief introduction to his work for a general mathematical audience.