Cédric Villani
Encyclopedia
Cédric Villani is a French
mathematician
working primarily on partial differential equations and mathematical physics
. He was awarded the Fields Medal
in 2010.
, Villani studied at the École Normale Supérieure
from 1992 to 1996, where he was appointed an assistant professor. He received his doctorate
at Paris Dauphine University in 1998, under the supervision of Pierre-Louis Lions
, and became professor at the École Normale Supérieure de Lyon
in 2000. He is now professor at Lyon University. He has been the director of Institut Henri Poincaré
in Paris since 2009.
, specifically the Boltzmann equation
, where, with Laurent Desvillettes, he was the first to prove how fast convergence occurred for initial values not near equilibrium. He has also written with Giuseppe Toscani on this subject. With Clément Mouhot, he has also worked on nonlinear Landau damping
. He has worked on the theory of optimal transport and its applications to differential geometry, and with John Lott
has defined a notion of bounded Ricci curvature
for general measured length spaces. He received the Fields Medal for his work on Landau damping
and the Boltzmann equation
.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
working primarily on partial differential equations and mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
. He was awarded the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
in 2010.
Biography
After attending the Lycée Louis-le-GrandLycée Louis-le-Grand
The Lycée Louis-le-Grand is a public secondary school located in Paris, widely regarded as one of the most rigorous in France. Formerly known as the Collège de Clermont, it was named in king Louis XIV of France's honor after he visited the school and offered his patronage.It offers both a...
, Villani studied at the École Normale Supérieure
École Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...
from 1992 to 1996, where he was appointed an assistant professor. He received his doctorate
Doctorate
A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder to teach in a specific field, A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder...
at Paris Dauphine University in 1998, under the supervision of Pierre-Louis Lions
Pierre-Louis Lions
Pierre-Louis Lions is a French mathematician. His parents were Jacques-Louis Lions, a mathematician and at that time professor at the University of Nancy, who in particular became President of the International Mathematical Union, and Andrée Olivier, his wife...
, and became professor at the École Normale Supérieure de Lyon
École Normale Supérieure de Lyon
The École Normale Supérieure de Lyon is a highly selective grande école located in Lyon, France. As one of France's three Écoles normales supérieures, ENS Lyon is associated with a strong French tradition of excellence and public service...
in 2000. He is now professor at Lyon University. He has been the director of Institut Henri Poincaré
Institut Henri Poincaré
The Institut Henri Poincaré is a mathematical institute in Paris which has established itself over its eighty year history as an important meeting place for French and international mathematicians and theoretical physicists...
in Paris since 2009.
Work
Villani has worked on the theory of partial differential equations involved in statistical mechanicsStatistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, specifically the Boltzmann equation
Boltzmann equation
The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...
, where, with Laurent Desvillettes, he was the first to prove how fast convergence occurred for initial values not near equilibrium. He has also written with Giuseppe Toscani on this subject. With Clément Mouhot, he has also worked on nonlinear Landau damping
Landau damping
In physics, Landau damping, named after its discoverer, the eminent Soviet physicist Lev Davidovich Landau, is the effect of damping of longitudinal space charge waves in plasma or a similar environment. This phenomenon prevents an instability from developing, and creates a region of stability in...
. He has worked on the theory of optimal transport and its applications to differential geometry, and with John Lott
John Lott (mathematician)
John Lott is a Professor of Mathematics at the University of California, Berkeley. He is working on Ricci flow....
has defined a notion of bounded Ricci curvature
Ricci curvature
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume element of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space...
for general measured length spaces. He received the Fields Medal for his work on Landau damping
Landau damping
In physics, Landau damping, named after its discoverer, the eminent Soviet physicist Lev Davidovich Landau, is the effect of damping of longitudinal space charge waves in plasma or a similar environment. This phenomenon prevents an instability from developing, and creates a region of stability in...
and the Boltzmann equation
Boltzmann equation
The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...
.
Awards
- Jacques Herbrand Prize (French Academy of Sciences) (2007)
- Prize of the European Mathematical SocietyEuropean Mathematical SocietyThe European Mathematical Society is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians...
(2008) - Fermat PrizeFermat PrizeThe Fermat prize of mathematical research rewards research works in fields where the contributions of Pierre de Fermat have been decisive:* Statements of variational principles* Foundations of probability and analytic geometry* Number theory....
(2009) - Henri Poincaré Prize (2009)
- Fields MedalFields MedalThe Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
(2010)
Selected writings
- Limites hydrodynamiques de l'équation de Boltzmann, Séminaire Bourbaki, June 2001; Astérisque vol. 282, 2002.
- A Review of Mathematical Topics in Collisional Kinetic Theory, in Handbook of Mathematical Fluid Dynamics, edited by S. Friedlander and D. Serre, vol. 1, Elsevier, 2002, ISBN 9780444503305. .
- Topics in Optimal Transportation, volume 58 of Graduate studies in mathematics, American Mathematical Society, 2003, ISBN 9780821833124.
- Optimal transportation, dissipative PDE’s and functional inequalities, pp. 53–89 in Optimal Transportation and Applications, edited by L. A. Caffarelli and S. Salsa, volume 1813 of Lecture Notes in Mathematics, Springer, 2003, ISBN 978-3-540-40192-6.
- Cercignani's conjecture is sometimes true and always almost true, Communications in Mathematical Physics, vol. 234, #3 (March 2003), pp. 455–490, .
- On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation (with Laurent Desvillettes), Inventiones Mathematicae, vol. 159, #2 (2005), pp. 245–316, .
- Mathematics of Granular Materials, Journal of Statistical Physics, vol. 124, #2-4 (July/August 2006), pp. 781–822, .
- Optimal transport, old and new, volume 338 of Grundlehren der mathematischen Wissenschaften, Springer, 2009, ISBN 9783540710493.
- Ricci curvature for metric-measure spaces via optimal transport (with John Lott), Annals of Mathematics vol. 169, #3 (2009), pp. 903–991.
- Hypocoercivity, volume 202, #950 of Memoirs of the American Mathematical Society, 2009, ISBN 9780821844984.