Cédric Patrice Thierry Villani (French: [se.dʁik pa.tʁis tje.ʁi vi.la.ni]; born 5 October 1973) is a French politician and mathematician 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.
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. 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, the lower house of the French Parliament, during the 2017 legislative election. He was elected as a member of La République En Marche! (REM), but in May 2020 left the party to form a new party, Ecology, Democracy, Solidarity. He was elected Vice President of the French 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. 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.
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 Clément 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. 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 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.
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. 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.