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 imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to poin ...

and

mathematical physics Mathematical physics refers to 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 t ...

. 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 the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

in 2010, and he was the director of

Sorbonne University Sorbonne University (french: Sorbonne Université; la Sorbonne: 'the Sorbonne') is a public research university located in Paris, France. The institution's legacy reaches back to 1257 when Sorbonne College was established by Robert de Sorbon ...

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 arrond ...

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. It is located in Bures-sur-Yvette, jus ...

. 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 Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to: * Kinetic theory, describing a gas as particles in random motion * Kinetic energy, the energy of an object that it possesses due to its motion Art and ente ...

and the one of the mathematician

Carlo Cercignani Carlo Cercignani (17 June 1939 in Teulada – 7 January 2010 in Milan) was an Italian mathematician known for his work on the kinetic theory of gases. His contributions to the study of Boltzmann's equation include the proof of the H-theorem fo ...

: 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 rep ...

, the lower house of the

French Parliament The French Parliament (french: Parlement français) is the bicameral legislature of the French Republic, consisting of the Senate () and the National Assembly (). Each assembly conducts legislative sessions at separate locations in Paris: ...

, during the 2017 legislative election.Emmanuel Macron team announces candidates for France's June parliamentary election

ABC News Online ABC News, or ABC News and Current Affairs, is a public news service produced by the Australian Broadcasting Corporation. Broadcasting within Australia and the rest of the world, the service covers both local and world affairs. The division of ...

, 12 May 2017. He was elected as a member of

La République En Marche! Renaissance (RE), previously known as La République En Marche ! (frequently abbreviated LREM, LaREM or REM; translated as "The Republic on the Move" or "Republic Forward"), or sometimes called simply En Marche ! () as its original name, is a l ...

(REM), 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 Ecology Generation (french: Génération écologie) is one of the four green parties in France, along with Europe Ecology – The Greens (), the Independent Ecological Movement (), and Cap Écologie. Founded in 1990 by Brice Lalonde, Environmen ...

, and ran for re-election under the banner of the

NUPES The New Ecological and Social People's Union (french: Nouvelle Union populaire écologique et sociale, link=no, NUPES) is a left-wing alliance of political parties in France. Formed on May Day 2022, the alliance includes La France Insoumise (LFI ...

. 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 Paul Midy (born 25 January 1983) is a French business executive and politician. A member of La République En Marche! (LREM), he is a member of the National Assembly for Essonne. Early life and education Midy was born in Fontainebleau. He stud ...

by 19 votes.

Biography

After attending the

Lycée Louis-le-Grand The Lycée Louis-le-Grand (), also referred to simply as Louis-le-Grand or by its acronym LLG, is a public Lycée (French secondary school, also known as sixth form college) located on rue Saint-Jacques in central Paris. It was founded in the ...

, Villani was admitted at the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

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 Paris Dauphine University - PSL (french: Université Paris-Dauphine, also known as Paris Dauphine - PSL or Dauphine - PSL) is a public research university based in Paris, France. It is one of the 13 universities formed by the division of the ancie ...

in 1998, under the supervision of

Pierre-Louis Lions Pierre-Louis Lions (; born 11 August 1956) is a French people, French mathematician. He is known for a number of contributions to the fields of partial differential equations and the calculus of variations. He was a recipient of the 1994 Fields Me ...

, and became professor at the

École normale supérieure de Lyon The École normale supérieure de Lyon (also known as ENS de Lyon, ENSL or Normale Sup' Lyon) is a French grande école located in the city of Lyon. It is one of the four prestigious écoles normales supérieures in France. The school is ...

in 2000. He is now professor at the

University of Lyon The University of Lyon (french: Université de Lyon), located in Lyon and Saint-Étienne, France, is a center for higher education and research comprising 11 members and 24 associated institutions. The three main universities in this center are: ...

. He was director of the

in Paris from 2009 to 2017. He has held various visiting positions at

Georgia Tech The Georgia Institute of Technology, commonly referred to as Georgia Tech or, in the state of Georgia, as Tech or The Institute, is a public research university and institute of technology in Atlanta, Georgia. Established in 1885, it is part of ...

(Fall 1999), the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

(Spring 2004), and the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...

(Spring 2009).

Mathematical work

Villani has worked on the theory of

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

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. It does not assume or postulate any natural laws, but explains the macroscopic be ...

, specifically the

Boltzmann equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerne ...

, 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 Clément Mouhot (; born 19 August 1978) is a French mathematician and academic. He is Professor of Mathematical Sciences at the University of Cambridge. His research is primarily in partial differential equations and mathematical physics (statis ...

, 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 a ...

. He has worked on the theory of

optimal transport In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources. The problem was formalized by the French mathematician Gaspard Monge in 1781.G. Monge. '' ...

and its applications to differential geometry, and with

John Lott John Richard Lott Jr. (born May 8, 1958) is an American economist, political commentator, and gun rights advocate. Lott was formerly employed at various academic institutions and at the American Enterprise Institute conservative think tank. He ...

has defined a notion of bounded

Ricci curvature In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measur ...

for general measured length spaces. He also served on the Mathematical Sciences jury for the

Infosys Prize The Infosys Prize is an annual award given to scientists, researchers, engineers and social scientists of Indian origin (not necessarily born in India) by the Infosys Science Foundation and ranks among the highest monetary awards in India to re ...

in 2015 and 2016. Villani received the Fields Medal for his work on

and the

. 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 TED Conferences, LLC (Technology, Entertainment, Design) is an American-Canadian non-profit media organization that posts international talks online for free distribution under the slogan "ideas worth spreading". TED was founded by Richard Sau ...

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), previously known as La République En Marche ! (frequently abbreviated LREM, LaREM or REM; translated as "The Republic on the Move" or "Republic Forward"), or sometimes called simply En Marche ! () as its original name, is a l ...

'' (LREM) in the 2017 French legislative election, 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

, 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, Member of the Strategic Committee

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 A miller is a person who operates a mill, a machine to grind a grain (for example corn or wheat) to make flour. Milling is among the oldest of human occupations. "Miller", "Milne" and other variants are common surnames, as are their equivalent ...

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 (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

) * 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 current ...

* 2009: Henri Poincaré Prize * 2009:

Fermat Prize The Fermat prize of mathematical research biennially rewards research works in fields where the contributions of Pierre de Fermat have been decisive: * Statements of variational principles * Foundations of probability and analytic geometry * Numb ...

* 2010:

* 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) * 2011: Knight of the

Legion of Honor The National Order of the Legion of Honour (french: Ordre national de la Légion d'honneur), formerly the Royal Order of the Legion of Honour ('), is the highest French order of merit, both military and civil. Established in 1802 by Napoleon ...

* 2013: Member of the

* 2016: Ordinary member of the

Pontifical Academy of Sciences The Pontifical Academy of Sciences ( it, Pontificia accademia delle scienze, la, Pontificia Academia Scientiarum) is a Academy of sciences, scientific academy of the Vatican City, established in 1936 by Pope Pius XI. Its aim is to promote the ...

* 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 Orb-weaver spiders are members of the spider family Araneidae. They are the most common group of builders of spiral wheel-shaped webs often found in gardens, fields, and forests. The English word "orb" can mean "circular", hence the English name ...

, ''

Araniella villanii ''Araniella'' is a genus of orb-weaver spiders (family Araneidae) first described by R. V. Chamberlin & Wilton Ivie in 1942. The genus includes '' Araniella cucurbitina'', the cucumber green spider. Species , the World Spider Catalog accepted t ...

'', 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 To ...

'', 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 Karol Beffa, born on October 27, 1973 in Paris, is a French and Swiss composer and pianist. Biography Karol Beffa had a general education along with music studies, at the Ecole Normale Supérieure in Paris, consisting of history, English, phi ...

) * ''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 Mathematical analysts 21st-century French mathematicians Fields Medalists Lycée Louis-le-Grand alumni École Normale Supérieure alumni Chevaliers of the Légion d'honneur PDE theorists Members of the French Academy of Sciences Institute for Advanced Study visiting scholars Paris Dauphine University alumni University of Lyon faculty Mathematical physicists French geometers La République En Marche! 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