Cédric Villani

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Cédric Villani
Cedric Villani at his office 2015 n3.jpg
Villani in 2015
Born (1973-10-05) 5 October 1973 (age 46)
Alma materÉcole Normale Supérieure
Paris Dauphine University
Known forBoltzmann equation
Kinetic theory
Landau damping
Transportation theory
Otto–Villani theorem
AwardsEMS Prize (2008)
Fermat Prize (2009)
Henri Poincaré Prize (2009)
Fields Medal (2010)
Joseph L. Doob Prize (2014)
Scientific career
InstitutionsInstitut Henri Poincaré, Sorbonne University
University of Lyon
Institut Camille-Jordan
ThesisContribution à l'étude mathématique des équations de Boltzmann et de Landau en théorie cinétique des gaz et des plasmas (1998)
Doctoral advisorPierre-Louis Lions
Doctoral studentsAlessio 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 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 University's Institut Henri Poincaré 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 Théorème 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 République En Marche! (REM), he represents Essonne's 5th constituency.[2] He was elected Vice 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, after which he was appointed an agrégé préparateur at the same school.[3] 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 was director of the Institut Henri Poincaré in Paris from 2009 to 2017.[4][5]

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).[6]

Mathematical work[edit]

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.[5] He has written with Giuseppe Toscani on this subject. With Clément Mouhot, he has worked on nonlinear Landau damping.[7] 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.[8]

Villani received the Fields Medal for his work on Landau damping and the Boltzmann equation.[5] 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.[9]

Political career[edit]

Cédric Villani at a public meeting of En Marche in Tokyo

In 2017, it was announced that Villani had been selected as a candidate for En Marche! (LREM) in the 2017 French legislative election, for Essonne's 5th constituency.[10][11] In the first round of voting, Villani obtained 47% of the vote and was thus strongly placed for the second round[12] which he won with 69.36% of the vote.[13]

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.[14] On September 4th, Villani officially announced his candidacy for the municipal election.[15]

Other activities[edit]

  • France China Foundation, Member of the Strategic Committee[16]

Awards and honours[edit]

Diplomas, titles and awards[edit]

Extra-academic distinctions[edit]

Selected writings[edit]

  • 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". Acta Mathematica. 207: 29–201. arXiv:0904.2760. doi:10.1007/s11511-011-0068-9.
  • 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. ^ Villani, Cédric. "Biography". Retrieved 11 April 2019.
  4. ^ Mathematics Genealogy Project – Cédric Villani. Accessed on line 20 August 2010.
  5. ^ a b c "Fields Medal – Cédric Villani". Archived from the original on 29 August 2010. Retrieved 20 August 2010.
  6. ^ "Curriculum Vitae (Cédric Villani)" (PDF). cedricvillani.org. Archived from the original (PDF) on 23 June 2016. Retrieved 24 May 2017.
  7. ^ Clément Mouhot; Cédric Villani (2010). "Landau damping". Journal of Mathematical Physics. 51 (15204): 015204. arXiv:0905.2167. Bibcode:2010JMP....51a5204M. doi:10.1063/1.3285283.
  8. ^ John Lott; Cedric Villani (2004). "Ricci curvature for metric-measure spaces via optimal transport". arXiv:math/0412127.
  9. ^ "Cédric Villani: What's so sexy about math?". TED. Retrieved 8 June 2016.
  10. ^ "France's Macron announces gender equal list of political outsiders". BBC News. 11 May 2017. Retrieved 11 May 2017.
  11. ^ "Communiqué de presse – Liste des investis aux élections législatives | En Marche !". En Marche !. Retrieved 11 May 2017.
  12. ^ "Cédric Villani : "L'idée, c'est d'avoir des compétences variées"". Libération. 15 June 2017. Retrieved 18 June 2017.
  13. ^ l'Intérieur, Ministère de. "Elections législatives 2017". elections.interieur.gouv.fr. Retrieved 19 June 2017.
  14. ^ Cosnard, Denis (10 July 2019). "Elections municipales à Paris: Benjamin Griveaux choisi pour représenter LRM". Le Monde (in French). Retrieved 3 August 2019.
  15. ^ à 19h11, Par R. Bx Le 4 septembre 2019; À 23h06, Modifié Le 4 Septembre 2019 (4 September 2019). "Municipales : Cédric Villani officialise sa candidature à la mairie de Paris". leparisien.fr (in French). Retrieved 5 September 2019.
  16. ^ Strategic Committee France China Foundation.
  17. ^ Josiah Willard Gibbs Lectures – No. 86, January 2013, San Diego, CA; Cédric Villani Accessed on line 20 May 2015.
  18. ^ Joseph L. Doob Prize – Most Recent Prize: 2014 Accessed on line 20 May 2015.
  19. ^ Cédric Villani, new member of the French Academy of Science Accessed on line 20 May 2015.

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