Tuesday, January 26, 2010

Ngo Bao Chau

Mathematician Ngo Bao Chau, who made one of Time magazine’s top 10 scientific discoveries of 2009, has accepted a faculty appointment at the University of Chicago. Ngô will become a professor of mathematics, effective Sept. 1, 2010.Ngo, 37, came to Time’s attention for decisive advances he recently made in two central areas of modern mathematics: number theory and representation theory.He proved a basic result, a matching conjecture called ‘the fundamental lemma,’ so named because it represents the central gate for progress in the Langlands program. Native of Hanoi, North Vietnam, Ngô received his doctoral degree from Université Paris-Sud in 1997. Currently a member of the Institute for Advanced Study in Princeton, N.J., Ngô received the Oberwolfach Prize in 2007, the Prix Sophie Germain de l’Académie des Sciences de Paris in 2007 and the Clay Research Award in 2004.In 1979 the Canadian-American mathematician Robert Langlands developed an ambitious and revolutionary theory that connected two branches of mathematics called number theory and group theory. In a dazzling set of conjectures and insights, the theory captured deep symmetries associated with equations that involve whole numbers, laying out what is now known as the Langlands.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. 1. Short curriculum vitae of Ngo Bao Chuoa•1972 born in Hanoi, Vietnam•1990 moves to France•1992-1995 student at the ENS, rue d’Ulm•1993-1997 doctoral studies at U. de Paris Sud, with G. Laumon•1997 dissertation ‘Le lemme fondamental de Jacquet et Ye’•1998-2004 charg´ de recherches au CNRS, at Univ. de Paris Norde•2004 Habilitation•2004– Professor U. de Paris-Sud•2006– IAS, Princeton•distinctions: Clay Research Award 2004, Speaker at ICM 2006.The conjecture of Langlands and Shelstad lies in the field of automorphic forms. Inthe beginning of the 20th century this theory was the theory of modular forms, i.e., ofholomorphic functions on the upper half plane transforming in a prescribed way under theaction of discrete groups of conformal motions. It was only in the 1950’s, under the influ-ence of I. Gelfand and Harish-Chandra, that the theory of automorphic forms on arbitrarysemi-simple Lie groups, or semi-simple algebraic groups, was developed. In the 1960’s thetheory was dramatically refocused through the introduction by R. Langlands of his func-toriality principle. This principle is a conjecture that stipulates correspondences betweenautomorphic forms on semi-simple groups which are related by a homomorphism betweentheir Langlands dual groups. This principle is surely among the most ingenious ideas ofthe last century and constitutes the deepest statement about automorphic forms known today.

No comments: