Gérard Laumon and Ngô Bao Châu
Clay Research Award 2004
Gérard Laumon and Ngô Bao Châu were recognized for their proof of the Fundamental Lemma for unitary groups. The lemma is a conjectured identity between orbital integrals for two groups, e.g., the unitary groups U(n) and U(p)xU(q), where p+q = n. Combined with the Arthur-Selberg trace formula, it enables one to prove relations between automorphic forms on different groups and is a key step towards proving links between certain automorphic forms and Galois representations. This is one of the aims of the Langlands program, which seeks a far-reaching unification of ideas in number theory and representation theory. The result of Laumon and Ngô uses the equivariant cohomology approach introduced by Goresky, Kottwitz, and MacPherson, who proved the lemma in the split and equal valuation case. The proof for the unitary case, which is significant for applications, requires many new ideas, including Laumon's deformation strategy and Ngô's purity result which is based on a geometric interpretation of the endoscopy theory of Langlands and Kottwitz in terms of the Hitchin fibration.
Gérard Laumon, born in Lyon in 1952, received his Thèse d'État from the Université de Paris-Sud, Orsay, in 1983 under the direction of Luc Illusie, his Directeur de Recherche. In 1987 Laumon was awarded the Silver Medal of CNRS. In 1992 he was awarded the E. Dechelle Prize of the French Academy of Sciences.
Ngô Bao Châu, born in 1972 in Hanoi, Vietnam, received his Ph.D. at the Université de Paris-Sud, Orsay, in 1997 under the direction of professor Gérard Laumon. He has held visiting positions at the Max Planck Institute in Bonn, the universities of Toronto, Sydney, and Chicago, and the Institut des Hautes Études Scientifiques (IHES). He has held a CNRS position at the Université de Paris 13 since 1998, and he assumed a professorship at the Université de Paris-Sud in the fall of 2004.