ⓘ Cédric Villani


ⓘ Cedric Villani

Cedric Patrice Thierry Villani is a French mathematician and politician working primarily on partial differential equations, Riemannian geometry and mathematical physics. He was awarded the Fields Medal in 2010 and he was the director of Sorbonne Universitys Institut Henri Poincare from 2009 to 2017.

In one of two lectures given at the Royal Institution, Villani recalled that his initial inspiration regarding the field of mathematics came from the 1959 Walt Disney cartoon Donald in Mathmagic Land. This lecture is titled Birth of a Theorem. The English translation of his book Theoreme vivant Living Theorem has the same title. His second lecture at the Royal Institution is titled The Extraordinary Theorems of John Nash.

Villani was elected to the National Assembly, the lower house of the French Parliament, during the 2017 legislative election. A member of La Republique En Marche! REM, he represents Essonnes 5th constituency. He was elected Vice President of the French Parliamentary Office for the Evaluation of Scientific and Technological Choices in July 2017.


1. Biography

After attending the Lycee Louis-le-Grand, Villani was admitted at the Ecole Normale Superieure in Paris and studied there from 1992 to 1996, after which he was appointed an agrege preparateur at 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 Ecole normale superieure de Lyon in 2000. He is now professor at the University of Lyon. He was director of the Institut Henri Poincare in Paris from 2009 to 2017.

He has held various visiting positions at Georgia Tech Fall 1999, the University of California, Berkeley Spring 2004, and the Institute for Advanced Study, Princeton Spring 2009.


2. Mathematical work

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. He has written with Giuseppe Toscani on this subject. With Clement Mouhot, he has 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.

Villani received the Fields Medal for his work on Landau damping and the Boltzmann equation. He described the development of his theorem in his autobiographical book Theoreme vivant 2012, published in English translation as Birth of a Theorem: A Mathematical Adventure 2015. He gave a TED talk at the 2016 conference in Vancouver.


3. Political career

In 2017, it was announced that Villani had been selected as a candidate for En Marche! LREM in the 2017 French legislative election, for Essonnes 5th constituency. In the first round of voting, Villani obtained 47% of the vote and was thus strongly placed for the second round which he won with 69.36% of the vote.

In 2019, Villani applied to be selected to lead the LREM candidate slate for the 2020 Paris election. By July 2019, he was one of three LREM candidates, all deputies in the National Assembly, still seeking the position; the other two were Benjamin Griveaux who had been the government spokesperson and Hugues Renson who had been the vice-president of the National Assembly. On 10 July, the nomination committee picked Griveaux. On September 4th, Villani officially announced his candidacy for the municipal election.


4.1. Awards and honours Diplomas, titles and awards

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


4.2. Awards and honours Extra-academic distinctions

  • 2013: Member of the French Academy of Sciences
  • 2016: Ordinary member of the Pontifical Academy of Sciences
  • 2009: Knight of the National Order of Merit France
  • 2011: Knight of the Legion of Honor

5. Selected writings

  • Les Coulisses de la creation, Flammarion, Paris 2015 with composer and pianist Karol Beffa
  • Optimal transport, old and new, volume 338 of Grundlehren der mathematischen Wissenschaften, Springer, 2009, ISBN 978-3-540-71049-3.
  • Ricci curvature for metric-measure spaces via optimal transport with John Lott, Annals of Mathematics vol. 169, No. 3 2009, pp. 903–991.
  • Freedom in Mathematics, Springer India, 2016, ISBN 978-81-322-2786-1. Translation from the French language edition: Mathematiques en liberte, La Ville Brûle, Montreuil 2012, ISBN 978-23-601-2026-0.
  • Cercignanis conjecture is sometimes true and always almost true, Communications in Mathematical Physics, vol. 234, No. 3 March 2003, pp. 455–490, doi:10.1007/s00220-002-0777-1.
  • Topics in Optimal Transportation, volume 58 of Graduate Studies in Mathematics, American Mathematical Society, 2003, ISBN 978-0-8218-3312-4.
  • Mathematics of Granular Materials, Journal of Statistical Physics, vol. 124, #2–4 July/August 2006, pp. 781–822, doi:10.1007/s10955-006-9038-6.
  • Hypocoercivity, volume 202, No. 950 of Memoirs of the American Mathematical Society, 2009, ISBN 978-0-8218-4498-4.
  • Theoreme vivant, Bernard Grasset, Paris 2012
  • 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, doi:10.1007/s00222-004-0389-9.
  • Clement Mouhot; Cedric Villani 2009. "On Landau damping". Acta Mathematica. 207: 29–201. arXiv: 0904.2760. doi:10.1007/s11511-011-0068-9.
  • Limites hydrodynamiques de lequation de Boltzmann, Seminaire Bourbaki, June 2001; Asterisque 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 978-0-444-50330-5. doi:10.1016/S1874-57920280004-0.
  • Optimal transportation, dissipative PDEs 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.