Paris, 19 August 2010

At the opening ceremony of the International Congress of Mathematicians, a quadrennial event gathering nearly 3,000 mathematicians from around the globe, Cédric Villani was awarded the 2010 Fields Medal, the equivalent of the Nobel Prize in mathematics. The 36-year-old Frenchman is a professor at the ENS (École Normale Supérieure) in Lyon, in the pure and applied mathematics unit (CNRS/ENS Lyon). Since 2009 he has also served as director of the Institut Henri Poincaré (CNRS/UPMC).

A graduate of the ENS in Paris, he completed his doctoral thesis at the Université Paris-Dauphine in 1998 under the supervision of Pierre-Louis Lions, himself a winner of the Fields Medal in 1994. Villani's research is based on the mathematical equations of the kinetic theory, which describes a system of interacting particles through a partial differential equation for the probability density of the presence of a "typical particle." An example of this situation is given by the study of a gas or fluid in which billions of molecules are moving in all directions. A series of projects undertaken by Villani have in large part responded to the physical and mathematical problem of extending this theory to long-range interactions.

Another of his fields of investigation is proving quantified forms of the second law of thermodynamics based on the Boltzmann equation. This equation made its originator, an Austrian physician and mathematician active in the late 19th century, famous for (among other things) providing mathematical "proof" of entropy growth. Villani's work, in cooperation with Laurent Desvillettes and Giuseppe Toscani, has made it possible to quantify entropy production and convergence to equilibrium. With Félix Otto, the medal winner also studied abstract metric structures (on probability space) in which to interpret dissipative equations.

In addition, Villani has worked with Clément Mouhot on "non-collisional relaxation", a phenomenon known in physics as Landau damping, named after the physicist who discovered it in 1946 and extensively studied since then. Villani has successfully proved this damping, first over very large time intervals—exponentially large in the perturbation size—and more recently on infinite time intervals. The results he has achieved have theoretical and practical ramifications, e.g. for classical mechanical models in astrophysics.

Cédric Villani has taken on difficult problems and produced impressive and sometimes unexpected results, forging new links between analysis and geometry. In 2009 he won the Fermat Prize and became the third French mathematician to receive the Henri Poincaré Prize from the International Association of Mathematical Physics.

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A graduate of the ENS in Paris, he completed his doctoral thesis at the Université Paris-Dauphine in 1998 under the supervision of Pierre-Louis Lions, himself a winner of the Fields Medal in 1994. Villani's research is based on the mathematical equations of the kinetic theory, which describes a system of interacting particles through a partial differential equation for the probability density of the presence of a "typical particle." An example of this situation is given by the study of a gas or fluid in which billions of molecules are moving in all directions. A series of projects undertaken by Villani have in large part responded to the physical and mathematical problem of extending this theory to long-range interactions.

Another of his fields of investigation is proving quantified forms of the second law of thermodynamics based on the Boltzmann equation. This equation made its originator, an Austrian physician and mathematician active in the late 19th century, famous for (among other things) providing mathematical "proof" of entropy growth. Villani's work, in cooperation with Laurent Desvillettes and Giuseppe Toscani, has made it possible to quantify entropy production and convergence to equilibrium. With Félix Otto, the medal winner also studied abstract metric structures (on probability space) in which to interpret dissipative equations.

In addition, Villani has worked with Clément Mouhot on "non-collisional relaxation", a phenomenon known in physics as Landau damping, named after the physicist who discovered it in 1946 and extensively studied since then. Villani has successfully proved this damping, first over very large time intervals—exponentially large in the perturbation size—and more recently on infinite time intervals. The results he has achieved have theoretical and practical ramifications, e.g. for classical mechanical models in astrophysics.

Cédric Villani has taken on difficult problems and produced impressive and sometimes unexpected results, forging new links between analysis and geometry. In 2009 he won the Fermat Prize and became the third French mathematician to receive the Henri Poincaré Prize from the International Association of Mathematical Physics.

© J.F. Dars

© Valérie Touchant-Landais/IHES

CNRS Press Officer l Elsa Champion l T 01 44 96 43 90 l elsa.champion@cnrs-dir.fr

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