Fields Medal – Cédric Villani

Cédric Villani is being awarded the 2010 Fields Medal for his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation.

Fields Medal – Cédric Villani, Institut Henri Poincaré

Fields Medal – Cédric Villani, Institut Henri Poincaré

One of the fundamental and initially very controversial theories of classical physics is Boltzmann’s kinetic theory of gases. Instead of tracking the individual motion of billions of individual atoms it studies the evolution of the probability that a particle occupies a certain position and has a certain velocity. The equilibrium probability distributions are well known for more than a hundred years, but to understand whether and how fast convergence to equilibrium occurs has been very difficult. Villani (in collaboration with Desvillettes) obtained the first result on the convergence rate for initial data not close to equilibrium. Later in joint work with his collaborator Mouhot he rigorously established the so-called non-linear Landau damping for the kinetic equations of plasma physics, settling a long-standing debate. He has been one of the pioneers in the applications of optimal transport theory to geometric and functional inequalities. He wrote a very timely and accurate book on mass transport.

Brief Biodata

Cédric Villani was born in 1973 in France. After studying mathematics at École Normale Supérieure in Paris from 1992 to 1996, he was appointed assistant professor there. He received his PhD in 1998. Since 2000 he has been a full professor at École Normale Supérieure de Lyon. He held semester-long visiting positions in Atlanta (1999), Berkeley (2004) and Princeton (2009), wrote about 50 research papers, and two reference books on optimal transport theory. His awards include the Jacques Herbrand Prize of the French Academy of Science (2007), the Prize of the European Mathematical Society (2008), the Henri Poincaré Prize of the International Association for Mathematical Physics, and the Fermat Prize (2009). In 2009 he was appointed director of the Institut Henri Poincaré (IHP) in Paris, and part-time visitor of the Institut des Hautes Études Scientifiques (IHES).


Email: cvillani at
Phone: (+33)1-4427-6418
Mailing address: Institut Henri Poincaré, 11 rue Pierre et Marie Curie 75230, Paris Cedex 05, FRANCE

The laudations by Hong-Tzer Yau
The work profile by Julie Rehmeyer

  This page was last modified on September 14, 2010

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