Bao Châu Ngô, Member in the School of Mathematics at the Institute for Advanced Study for the last three and a half years, has been awarded the Fields Medal in Hyderabad, India, at the International Congress of Mathematicians for his proof of the fundamental lemma. The other recipients of Fields Medals this year have also been Members of the Institute—Elon Lindenstrauss (2000–01, 2007) received the award for his results on measure rigidity in ergodic theory, and their applications to number theory; Stanislav Smirnov (1998, 2003) was recognized for the proof of conformal invariance of percolation and the planar Ising model in statistical physics; Cédric Villani (2009) was selected for his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation.
The Chern Medal was awarded in recognition of lifelong outstanding achievement in mathematics to Louis Nirenberg, Professor Emeritus at New York University’s Courant Institute of Mathematical Sciences and a former Visitor (1979–80) in the School.
The award laudation called Ngô’s proof of the fundamental lemma “a profound and beautiful argument, built on insights mathematicians have contributed for over thirty years.” The fundamental lemma, a technical device that links automorphic representations of different groups, was formulated more than 30 years ago by Robert Langlands, Professor Emeritus in the School of Mathematics at the Institute, and emerged from a set of overarching and interconnected conjectures that link number theory and representation theory, collectively known as the Langlands program. Over the years, it became clear that the fundamental lemma was extremely difficult to prove in the general case, although progress was made in specific cases through work done by Langlands, his students and others at the Institute and elsewhere. A recent article in the Institute Letter examines the fundamental lemma in some detail.
Ngô’s proof of the fundamental lemma, confirmed last fall, is based on a geometric interpretation of endoscopy theory. It follows the work of many mathematicians associated with the Institute over the past three decades, including Robert MacPherson, Hermann Weyl Professor in the School, current Member Mark Goresky and former Members Thomas Hales, Hervé Michel Jacquet, Robert Kottwitz, Jean-Pierre Labesse, Gérard Laumon, Jonathan Rogawski, Diana Shelstad and Rainer Weissauer.
“The awarding of the Fields Medal to Ngô, Lindenstrauss, Smirnov and Villani is a very fitting recognition of the outstanding contributions they have made to mathematics through great insight and persistence,” said Peter Goddard, Director of the Institute. “It is also a testament to the opportunities the Institute provides for scholars to pursue long-term goals free from the pressure for immediate results. We are delighted in particular that Ngô’s success follows in the great traditions of the Institute established through the work of Hermann Weyl, Robert Langlands, Harish-Chandra and others.”
Born in Vietnam, Ngô received his Ph.D. from the Université Paris-Sud in 1997 under the direction of Gérard Laumon and received his Habilitation in 2004 from the Université Paris 13. In 2004, Ngô and Laumon were recognized with the Clay Research Award for their proof of the fundamental lemma for unitary groups. Ngô 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 (IHÉS). From 1998 to 2004, Ngô held a position at CNRS, the French National Center for Scientific Research, at the Université Paris 13, and he was a Professor at the Université Paris-Sud from 2005–10. This fall he will join the faculty of the University of Chicago.
Lindenstrauss, Professor of Mathematics at Princeton University and the Hebrew University of Jerusalem, was cited for work of “power and beauty” that “continues a tradition of interaction between dynamical systems theory and diophantine analysis.” Smirnov, Professor of Mathematics at the Université de Genève, was cited for “his ingenious and astonishing work on the existence and conformal invariance of scaling limits or continuum limits of lattice models in statistical physics.” Villani, director of the Henri Poincaré Institute of the Université Pierre et Marie Curie in Paris, was recognized for results arising from the fundamental connection between entropy and its dissipation, in work showing “not only rigorous mathematical analysis providing deep insights into physical behavior, but also important new mathematics emerging from the study of natural phenomena.”
Also at the International Congress of Mathematicians, it was announced that Ingrid Daubechies, a former Member (1999) and an organizer of the Women and Mathematics program at the Institute, was elected president of the International Mathematical Union. Daubechies, who will be the first woman to hold this position, is William R. Kenan Jr. Professor of Mathematics and Applied Computational Mathematics at Princeton University.
The Fields Medal is the world’s highest award for achievement in mathematics and is presented every four years by the International Mathematical Union. Since 1936, the Fields Medal has been presented to 52 individuals, of whom 38 have been either Faculty members or visiting scientists at the Institute for Advanced Study. The Fields Medal is awarded to young mathematicians, aged 40 or under, for outstanding mathematical achievement, and recognizes both existing work and the promise of future achievement. It is generally shared by four individuals.
About the Institute for Advanced Study
The Institute for Advanced Study is one of the world’s leading centers for theoretical research and intellectual inquiry. The Institute exists to encourage and support curiosity-driven research in the sciences and humanities—the original, often speculative thinking that produces advances in knowledge that change the way we understand the world. Work at the Institute takes place in four Schools: Historical Studies, Mathematics, Natural Sciences and Social Science. It provides for the mentoring of scholars by a permanent Faculty of approximately 30, and it ensures the freedom to undertake research that will make significant contributions in any of the broad range of fields in the sciences and humanities studied at the Institute.
The Institute, founded in 1930, is a private, independent academic institution located in Princeton, New Jersey. Its more than 6,000 former Members hold positions of intellectual and scientific leadership throughout the academic world. Thirty-three Nobel Laureates and 40 out of 56 Fields Medalists, as well as many winners of the Wolf and MacArthur prizes, have been affiliated with the Institute.