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 44)
Brive-la-Gaillarde, France[1]
Residence Paris, France
Nationality French
Alma mater École Normale Supérieure
Paris Dauphine University
Known for Boltzmann equation
Kinetic theory
Landau damping
Transportation theory
Otto–Villani theorem
Awards EMS Prize (2008)
Fermat Prize (2009)
Henri Poincaré Prize (2009)
Fields Medal (2010)
Joseph L. Doob Prize (2014)
Website cedricvillani.org
Scientific career
Fields Mathematics
Institutions Institut Henri Poincaré, Pierre and Marie Curie University
University of Lyon
Institut Camille Jordan
Thesis Contribution à l'étude mathématique des équations de Boltzmann et de Landau en théorie cinétique des gaz et des plasmas (1998)
Doctoral advisor Pierre-Louis Lions
Doctoral students Alessio Figalli
Clément Mouhot

Cédric Patrice Thierry Villani (French: [se.dʁik pa.tʁis tjɛ.ʁi vi.la.ni]; 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 and is the director of Pierre and Marie Curie University's Institut Henri Poincaré.

Villani is also a politician. He sits in the National Assembly, the lower house of the French Parliament, representing Essonne's 5th constituency for En Marche!, the centrist political party of the French president Emmanuel Macron which currently holds the majority following the 2017 French legislative election.[2] He was elected president of the French Parliamentary Office for the Evaluation of Scientific and Technological Choices in July 2017.


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 the University of Lyon. He has been the director of Institut Henri Poincaré in Paris since 2009.[3][4]

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).[5]

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.[4] He has written with Giuseppe Toscani on this subject. With Clément Mouhot, he has worked on nonlinear Landau damping.[6] 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.[7]

Villani received the Fields Medal for his work on Landau damping and the Boltzmann equation.[4] 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). He gave a TED talk at the 2016 conference in Vancouver.[8]

Political career

In 2017, it was announced that Villani has been selected as a candidate for En Marche! in the French legislative election, 2017, for Essonne's 5th constituency.[9][10] In the first round of voting, Villani obtained 47% of the vote and was thus strongly placed for the second round[11] which he won with 69.36% of the vote.[12]

Awards and honours

Diplomas, titles and awards

Extra-academic distinctions

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 978-0-444-50330-5. doi:10.1016/S1874-5792(02)80004-0.
  • Topics in Optimal Transportation, volume 58 of Graduate Studies in Mathematics, American Mathematical Society, 2003, ISBN 978-0-8218-3312-4.
  • 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, No. 3 (March 2003), pp. 455–490, doi:10.1007/s00220-002-0777-1.
  • 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.
  • 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.
  • 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.
  • Hypocoercivity, volume 202, No. 950 of Memoirs of the American Mathematical Society, 2009, ISBN 978-0-8218-4498-4.
  • Clément Mouhot; Cédric Villani (2009). "On Landau damping". arXiv:0904.2760Freely accessible [math.AP]. 
  • Théorème vivant, Bernard Grasset, Paris 2012
  • Les Coulisses de la création, Flammarion, Paris 2015 (with composer and pianist Karol Beffa)
  • Freedom in Mathematics, Springer India, 2016 (with Pierre Cartier, Jean Dhombres, Gerhard Heinzmann), ISBN 978-81-322-2786-1.
    • Translation from the French language edition: Mathématiques en liberté, La Ville Brûle, Montreuil 2012, ISBN 978-23-601-2026-0.


  1. ^ Sylvain Guilbaud; Antoine Walraet. "Cédric Villani", Encyclopædia Universalis.
  2. ^ Emmanuel Macron team announces candidates for France's June parliamentary election, ABC News Online, 12 May 2017
  3. ^ Mathematics Genealogy Project – Cédric Villani. Accessed on line 20 August 2010.
  4. ^ a b c "Fields Medal – Cédric Villani". Archived from the original on 29 August 2010. Retrieved 20 August 2010. 
  5. ^ "Curriculum Vitae (Cédric Villani)" (PDF). http://cedricvillani.org. Retrieved 24 May 2017.  External link in |website= (help)
  6. ^ Clément Mouhot; Cédric Villani (2010). "Landau damping". Journal of Mathematical Physics. 51 (15204): 015204. arXiv:0905.2167Freely accessible. doi:10.1063/1.3285283. 
  7. ^ John Lott; Cedric Villani (2004). "Ricci curvature for metric-measure spaces via optimal transport". arXiv:math/0412127Freely accessible [math.DG]. 
  8. ^ "Cédric Villani: What's so sexy about math?". TED. Retrieved 8 June 2016. 
  9. ^ "France's Macron announces gender equal list of political outsiders". BBC News. 11 May 2017. Retrieved 11 May 2017. 
  10. ^ "Communiqué de presse – Liste des investis aux élections législatives | En Marche !". En Marche !. Retrieved 11 May 2017. 
  11. ^ "Cédric Villani : "L'idée, c'est d'avoir des compétences variées"". Libération. 15 Jun 2017. Retrieved 18 Jun 2017. 
  12. ^ l'Intérieur, Ministère de. "Elections législatives 2017". elections.interieur.gouv.fr. Retrieved 2017-06-19. 
  13. ^ Josiah Willard Gibbs Lectures – No. 86, January 2013, San Diego, CA; Cédric Villani Accessed on line 20 May 2015.
  14. ^ Joseph L. Doob Prize – Most Recent Prize: 2014 Accessed on line 20 May 2015.
  15. ^ Cédric Villani, new member of the French Academy of Science Accessed on line 20 May 2015.

External links

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