Cédric Villani

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Cédric Villani
Cedric Villani at his office 2015 n3.jpg
Cédric Villani in 2015
Born (1973-10-05) 5 October 1973 (age 42)
Brive-la-Gaillarde, France[1]
Residence Paris, France
Nationality French
Fields Mathematics
Institutions Institut Camille Jordan
Institut Henri Poincaré
Claude Bernard University Lyon 1
Alma mater École Normale Supérieure, Paris Dauphine University
Doctoral advisor Pierre-Louis Lions
Doctoral students Alessio Figalli
Clément Mouhot
Known for Boltzmann equation
Kinetic theory
Landau damping
Transportation theory
Otto–Villani theorem
Notable awards EMS Prize (2008)
Fermat Prize (2009)
Henri Poincaré Prize (2009)
Fields Medal (2010)

Cédric Villani (born 5 October 1973) is a French mathematician working primarily on partial differential equations, Riemannian geometry and mathematical physics. He was awarded the Fields Medal in 2010.


After attending the Lycée Louis-le-Grand, Villani was admitted at the École normale supérieure in Paris and studied there from 1992 to 1996. He was later appointed an assistant professor in the same school. 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.[2][3]


Villani has worked on the theory of partial differential equations involved in statistical mechanics, specifically the Boltzmann equation, where, with Laurent Desvillettes, he was the first to prove how quickly convergence occurs for initial values not near equilibrium.[3] He has also written with Giuseppe Toscani on this subject. With Clément Mouhot, he has also worked on nonlinear Landau damping.[4] 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.[5]

He received the Fields Medal for his work on Landau damping and the Boltzmann equation.[3] He described the development of his theorem in his autobiographical book Théorème vivant (2012), published in English translation as Birth of a Theorem: A Mathematical Adventure (2015).

Awards and honors[edit]

Diplomas, titles and awards[edit]

  • 1998: PhD Thesis (advisor P.-L. Lions)
  • 2000: Habilitation dissertation
  • 2001: Louis Armand Prize of the Academy of Sciences
  • 2003: Peccot-Vimont Prize and Cours Peccot of the Collège de France
  • 2003: Plenary lecturer at the International Congress of Mathematical Physics (Lisbonne)
  • 2004: Harold Grad lecturer
  • 2006: Institut Universitaire de France
  • 2006: Invited lecturer at the International Congress of Mathematicians (Madrid)
  • 2007: Jacques Herbrand Prize (French Academy of Sciences)
  • 2008: Prize of the European Mathematical Society
  • 2009: Henri Poincaré Prize
  • 2009: Fermat Prize
  • 2010: Fields Medal
  • 2013: Gibbs lecturer: On Disorder, Mixing and Equilibration[6]
  • 2014: Joseph L. Doob Prize by the American Mathematical Society for his book Optimal Transport: Old and New (Springer Verlag 2009)[7]

Extra-academic distinctions[edit]

Selected writings[edit]


  1. ^ Sylvain Guilbaud; Antoine Walraet. "Cédric Villani", Encyclopædia Universalis.
  2. ^ Mathematics Genealogy Project – Cédric Villani. Accessed on line 20 August 2010.
  3. ^ a b c Fields Medal – Cédric Villani. Accessed on line 20 August 2010
  4. ^ Clément Mouhot; Cédric Villani (2010). "Landau damping". Journal of Mathematical Physics 51 (15204): 015204. arXiv:0905.2167. doi:10.1063/1.3285283. 
  5. ^ John Lott; Cedric Villani (2004). "Ricci curvature for metric-measure spaces via optimal transport". arXiv:math/0412127 [math.DG]. 
  6. ^ Josiah Willard Gibbs Lectures - No. 86, January 2013, San Diego, CA; Cédric Villani Accessed on line 20 May 2015.
  7. ^ Joseph L. Doob Prize - Most Recent Prize: 2014 Accessed on line 20 May 2015.
  8. ^ Cédric Villani, new member of the French Academy of Science Accessed on line 20 May 2015.

External links[edit]