Ngô Bảo Châu is being awarded the 2010 Fields Medal for for his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods.
In the 1960’s and 70’s Robert Langlands formulated various basic unifying principles and conjectures relating automorphic forms on different groups, Galois representations and L-functions. These led to what today is referred to as the Langlands programme. The main tool in establishing some cases of these conjectures is the trace formula and in applying it for the above purposes a central difficulty intervenes: to establish some natural identities in harmonic analysis on local groups as well as ones connected to arithmetic geometric objects. This problem became known as the Fundamental Lemma. After many advances by a number of researchers in 2004, Laumon and Ngô established the Fundamental Lemma for a special family of groups, and recently Ngô established the Lemma in general.
Ngô’s brilliant proof of this important long standing conjecture is based in part on the introduction of novel geometric objects and techniques into this sophisticated analysis. His achievement, which lies at the crossroads between algebraic geometry, group theory and automorphic forms, is leading to many striking advances in the Langlands programme as well as the subjects linked with it.
Ngô Bảo Châu was born on June 28, 1972, in Hanoi, Vietnam. After secondary school in Vietnam, he moved to France and studied at the Université Paris 6, Ecole Normale Supérieure de Paris. He completed his PhD Degree in Orsay under the supervision of Gérard Laumon. He is currently Professor in the Faculté des Sciences at Orsay and Member of the Institute for Advanced Study in Princeton. In September 2010, he will start his new appointment at the University of Chicago. Jointly with Laumon, Ngô was awarded the Clay research award in 2004. In 2007, he was awarded the Sophie Germain prize and the Oberwolfach prize.