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Cédric Patrice Thierry Villani (; born 5 October 1973) is a French politician and mathematician working primarily on
partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...
s,
Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as manifold, smooth manifolds with a ''Riemannian metric'' (an inner product on the tangent space at each point that varies smooth function, smo ...
and
mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...
. He was awarded the
Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...
in 2010, and he was the director of Sorbonne University's
Institut Henri Poincaré The Henri Poincaré Institute (or IHP for ''Institut Henri Poincaré'') is a mathematics research institute part of Sorbonne University, in association with the Centre national de la recherche scientifique (CNRS). It is located in the 5th arrondi ...
from 2009 to 2017. As of September 2022, he is a professor at
Institut des Hautes Études Scientifiques The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics (also with a small theoretical biology g ...
. Villani has given two lectures at the Royal Institution, the first titled 'Birth of a Theorem'. The English translation of his book ''Théorème vivant'' (''Living Theorem'') has the same title. In the book he describes the links between his research on kinetic theory and that of the mathematician Carlo Cercignani: Villani, in fact, proved the so-called Cercignani's conjecture. His second lecture at the Royal Institution is titled 'The Extraordinary Theorems of John Nash'. Villani was elected as the deputy for Essonne's 5th constituency in the
National Assembly In politics, a national assembly is either a unicameral legislature, the lower house of a bicameral legislature, or both houses of a bicameral legislature together. In the English language it generally means "an assembly composed of the repr ...
, the lower house of the
French Parliament The French Parliament (, ) is the Bicameralism, bicameral parliament of the French Fifth Republic, consisting of the Senate (France), Senate (), and the National Assembly (France), National Assembly (). Each assembly conducts legislative sessi ...
, during the 2017 legislative election.Emmanuel Macron team announces candidates for France's June parliamentary election
ABC News Online, 12 May 2017.
He was elected as a member of La République En Marche! (LREM), but in May 2020 left the party to form a new party, Ecology, Democracy, Solidarity (EDS). Following the dissolution of EDS, Villani joined Ecology Generation, and ran for re-election under the banner of the NUPES. He was elected vice president of the French Parliamentary Office for the Evaluation of Scientific and Technological Choices in July 2017. He lost his seat in the 2022 French legislative election to La Republique En Marche! candidate Paul Midy by 19 votes.


Biography

After attending the Lycée Louis-le-Grand, Villani was admitted at the
École Normale Supérieure École or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...
in Paris and studied there from 1992 to 1996, after which he was appointed an agrégé préparateur 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 École normale supérieure de Lyon in 2000. He is now professor at the University of Lyon. He was director of the
Institut Henri Poincaré The Henri Poincaré Institute (or IHP for ''Institut Henri Poincaré'') is a mathematics research institute part of Sorbonne University, in association with the Centre national de la recherche scientifique (CNRS). It is located in the 5th arrondi ...
in Paris from 2009 to 2017. He has held various visiting positions at Georgia Tech (Fall 1999), the
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...
(Spring 2004), and the
Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...
, Princeton (Spring 2009). On 19 October 2014, in the context of the Cultural Services of the French Embassy's inaugural Albertine festival, Villani appeared in conversation with the
Nobel Prize The Nobel Prizes ( ; ; ) are awards administered by the Nobel Foundation and granted in accordance with the principle of "for the greatest benefit to humankind". The prizes were first awarded in 1901, marking the fifth anniversary of Alfred N ...
winning mathematician John F. Nash, Jr. Several months later, on 23 May 2015, Nash, along with his wife, Alicia died in a car crash. Speaking at the
Hay Festival The Hay Festival of Literature & Arts, better known as the Hay Festival (), is an annual literature festival held in Hay-on-Wye, Powys, Wales, for 10 days from May to June. Devised by Norman, Rhoda and Peter Florence in 1988, the festival was d ...
, just days after Nash's death, Villani announced that Nash told Villani, in Norway on 20 May, that he had found a 'replacement equation' for Einstein's theory of relativity.


Mathematical work

Villani has worked on the theory of
partial differential equations In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how ...
involved in
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
, 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 Clément Mouhot, he has worked on nonlinear
Landau damping In physics, Landau damping, named after its discoverer,Landau, L. "On the vibration of the electronic plasma". ''JETP'' 16 (1946), 574. English translation in ''J. Phys. (USSR)'' 10 (1946), 25. Reproduced in Collected papers of L.D. Landau, edited ...
. 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 also served on the Mathematical Sciences jury for the Infosys Prize in 2015 and 2016. Villani received the Fields Medal for his work on
Landau damping In physics, Landau damping, named after its discoverer,Landau, L. "On the vibration of the electronic plasma". ''JETP'' 16 (1946), 574. English translation in ''J. Phys. (USSR)'' 10 (1946), 25. Reproduced in Collected papers of L.D. Landau, edited ...
and the Boltzmann equation. 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.


Political career

In 2017, it was announced that Villani had been selected as a candidate for ''
En Marche! Renaissance (RE) is a List of political parties in France, political party in France that is typically described as liberalism, liberal and centrist or centre-right. The party was originally known as (EM) and later (, LREM, LaREM or REM), be ...
'' (LREM) in the
2017 French legislative election Legislative elections in France, Legislative elections were held in France on 11 and 18 June 2017 (with different dates for voters overseas) to elect the 577 Member of Parliament (France), members of the 15th legislature of the French Fifth Rep ...
, for Essonne's 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 In politics, a national assembly is either a unicameral legislature, the lower house of a bicameral legislature, or both houses of a bicameral legislature together. In the English language it generally means "an assembly composed of the repr ...
, 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 4 September, Villani officially announced his candidacy for the municipal election.


Other activities

* France China Foundation, former Member of the Strategic Committee In December 2024, the French
economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...
magazine A magazine is a periodical literature, periodical publication, print or digital, produced on a regular schedule, that contains any of a variety of subject-oriented textual and visual content (media), content forms. Magazines are generally fin ...
Challenges says that Villani has been approached by Europanova thinktank. He presided over the jury of Digital In-Pulse, a startup program dedicated to accompanying entrepreneurs and start-ups, managed by Chinese
corporate A corporation or body corporate is an individual or a group of people, such as an association or company, that has been authorized by the state to act as a single entity (a legal entity recognized by private and public law as "born out of s ...
Huawei Huawei Technologies Co., Ltd. ("Huawei" sometimes stylized as "HUAWEI"; ; zh, c=华为, p= ) is a Chinese multinational corporationtechnology company in Longgang, Shenzhen, Longgang, Shenzhen, Guangdong. Its main product lines include teleco ...
. The magazine also says that Villani is still the President of the endowment funds of the French Henri Poincaré Institute, and
Huawei Huawei Technologies Co., Ltd. ("Huawei" sometimes stylized as "HUAWEI"; ; zh, c=华为, p= ) is a Chinese multinational corporationtechnology company in Longgang, Shenzhen, Longgang, Shenzhen, Guangdong. Its main product lines include teleco ...
is among the top private donors. Villani declined the journalist's request for comment, and the article indicates that the French
counter-intelligence Counterintelligence (counter-intelligence) or counterespionage (counter-espionage) is any activity aimed at protecting an agency's intelligence program from an opposition's intelligence service. It includes gathering information and conducting ac ...
service presented him as "too naïve" regarding those opportunities.


Awards and honours


Diplomas, titles and awards

* 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 * 2004: Visiting Miller Professor, University of California Berkeley. * 2006: Institut Universitaire de France * 2006: Invited lecturer at the International Congress of Mathematicians (Madrid) * 2007: (
French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...
) * 2008: Prize of the
European Mathematical Society The European Mathematical Society (EMS) 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. The curren ...
* 2009:
Henri Poincaré Prize The Henri Poincaré Prize is awarded every three years since 1997 for exceptional achievements in mathematical physics and foundational contributions leading to new developments in the field. It is named after the French mathematician Henri Poincar ...
* 2009: Fermat Prize * 2010:
Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...
* 2013: Gibbs lecturer: ''On Disorder, Mixing and Equilibration'' * 2014: Joseph L. Doob Prize by the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
for his book ''Optimal Transport: Old and New'' (Springer Verlag 2009)


Extra-academic distinctions

* 2009: Knight of the
National Order of Merit (France) National Order of Merit may refer to: * National Order of Merit (Algeria) * National Order of Merit (Bhutan) * National Order of Merit (Brazil) * National Order of Merit (Ecuador) * Ordre national du Mérite (France) * National Order of Merit ...
* 2011: Knight of the Legion of Honor * 2013: Member of the
French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...
* 2016: Ordinary member of the Pontifical Academy of Sciences * 2022: Fellow of the
International Science Council The International Science Council (ISC) is an international non-governmental organization that unites scientific bodies at various levels across the social and natural sciences. The ISC was formed with its inaugural general assembly on 4 July 20 ...
In 2020, a new spider species of the family Araneidae, '' Araniella villanii'', was named after him.


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, . . * ''Topics in Optimal Transportation'', volume 58 of ''
Graduate Studies in Mathematics Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS). The books in this series are published ihardcoverane-bookformats. List of books *1 ''The General T ...
'', American Mathematical Society, 2003, . * 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, . * Cercignani's conjecture is sometimes true and always almost true, ''Communications in Mathematical Physics'', vol. 234, No. 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, .
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, . * * ''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), . Translation from the French language edition: ''Mathématiques en liberté'', La Ville Brûle, Montreuil 2012, . * ''Birth of a Theorem'', Farrar, Straus and Giroux, New York 2015; translated by Malcolm DeBevoise. * ''De mémoire vive'', Une histoire de l'aventure numérique, Philippe Dewost, Cédric Villani, Éditions Première Partie, 2022, .


References


External links


Cédric Villani's website
*
Video Interview by ICTP

Review of 'Birth of a Theorem'
{{DEFAULTSORT:Villani, Cedric 1973 births Living people French people of Italian descent People from Brive-la-Gaillarde 20th-century French mathematicians French mathematical analysts 21st-century French mathematicians Fields Medalists Lycée Louis-le-Grand alumni École Normale Supérieure alumni Knights of the Legion of Honour Partial differential equation theorists Members of the French Academy of Sciences Institute for Advanced Study visiting scholars Paris Dauphine University alumni Academic staff of the University of Lyon French mathematical physicists French geometers Renaissance (French political party) politicians Ecology Democracy Solidarity politicians Deputies of the 15th National Assembly of the French Fifth Republic Young Leaders of the French-American Foundation Members of Parliament for Essonne