Top Young Mathematicians Receive Prestigious Fields Medal 

The Fields Medal is the world’s highest award for achievement in mathematics. Courtesy of Stefan Zachow, Konrad-Zuse-Zentrum für Informationstechnik Berlin

Regarded as the “Nobel Prize of Mathematics,” the Fields Medal is presented once every four years to as many as four people under the age of 40. The purpose of the prize is to recognize and reward young mathematical researchers who have made major contributions to the field. It is the world’s highest award for achievement in mathematics. Since 1936, the Fields Medal has been presented to 52 individuals in recognition of both existing work and the promise of future achievement.

On August 9, 2010, the International Congress of the International Mathematical Union awarded the prestigious Fields Medal to four mathematicians:

• Bao Châu Ngô, a 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 for his proof of the fundamental lemma.

• Elon Lindenstrauss, of Princeton University and a member at the Institute for Advanced Study from 2000–01 and 2007, received the award for his results on measure rigidity in ergodic theory, and their applications to number theory.

• Stanislav Smirnov, a member at the Institute for Advanced Study in 1998 and 2003, was recognized for the proof of conformal invariance of percolation and the planar Ising model in statistical physics.

• Cédric Villani, a member at the Institute for Advanced Study in 2009, was selected for his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation.

In addition, 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 of Mathematics at the Institute for Advanced Study.

The award laudation called Ngô’s proof of the fundamental lemma “a profound and beautiful argument, built on insights mathematicians have contributed for over 30 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 for Advanced Study, 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.

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.”

Two of the awardees, Elon Lindenstrauss and Ngô B?o Châu are currently supported by research grants from the National Science Foundation (NSF). A third recipient, Stanislav Smirnov, received trainee support from NSF for graduate studies and post-doctoral work while in the United States.