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2004 Clay Research Awards Announced
November 5, 2004
CAMBRIDGE, MA - The Clay Mathematics Institute (CMI) announced the 2004 Clay Research Awards at its Annual Meeting held on Friday, November 5 at Harvard University. The awards, which recognize significant recent research breakthroughs in mathematics, were presented to Ben Green of Trinity College, Cambridge, and to Gérard Laumon and Bao-Châu Ngô, both of the Université de Paris-Sud and the CNRS (Centre Nationale de Recherche Scientifique).
Ben Green was recognized for his joint work with Terry Tao on arithmetic progressions of prime numbers. These are equally spaced sequences of primes such as 31, 37, 43 or 13, 43, 73, 103. Results in the area go back to the work of Lagrange and Waring in the 1770's. A major breakthrough came in 1939 when the Dutch mathematician Johannes van der Corput showed that there are an infinite number of three-term arithmetic progressions of primes. Green and Tao showed that for any n, there are infinitely many n-term progressions of primes. Their proof, which relies on results of Szemerédi (1975) and Goldston and Yldirim (2003), uses ideas from combinatorics, ergodic theory, and the theory of pseudorandom numbers. The Green-Tao result is a major advance in our understanding of the primes.
Laumon and Ngô 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.
Ben Green was named a Clay Research Fellow for a term of two years. Laumon and Ngô were named Clay Research Scholars for a period of one year. All received a bronze replica of the CMI icon by sculptor Helaman Ferguson. Former recipients of the Clay Research Award are: Andrew Wiles, Laurent Lafforgue, Alain Connes, Stanislav Smirnov, Edward Witten, Oded Schramm, Manindra Agrawal, Richard Hamilton, and Terence Tao.
Ben Green was born in 1977 in Bristol, England. He was educated at Trinity College, Cambridge first as an undergraduate and later as a research student of Fields Medalist Tim Gowers. Since 2001 he has been a Fellow of Trinity College, and in that time he has visited Princeton, the Rényi Institute in Budapest and the University of British Columbia, Vancouver, for extended periods. In January 2005 he will take up a Chair in Pure Mathematics at the University of Bristol.
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.
Bao-Châu Ngô, born in 1972 in Hanoi, Vietnam, received his Ph.D. at the Universit&ecute; 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.