Villani has given two lectures at theRoyal Institution, the first titled 'Birth of a Theorem'.[3] The English translation of his bookThéorème vivant (Living Theorem) has the same title. In the book he describes the links between his research onkinetic theory and that of the mathematicianCarlo Cercignani. Villani, in fact, proved the so-calledCercignani's conjecture.
His second lecture at the Royal Institution is titled 'The Extraordinary Theorems ofJohn Nash'.[4]
On 19 October 2014, in the context of the Cultural Services of the French Embassy's inauguralAlbertine festival, Villani appeared in conversation with theNobel Prize winning mathematicianJohn F. Nash, Jr.[14]
Several months later, on 23 May 2015, Nash, along with his wife Alicia, died in a car crash. Speaking at theHay Festival, just days after his death, Villani announced that Nash had told him, in Norway on 20 May, that he had found a 'replacement equation' forEinstein's theory of relativity.[15]
Villani has worked on the theory ofpartial differential equations involved instatistical mechanics, specifically theBoltzmann equation, where, with Laurent Desvillettes, he was the first to prove how quickly convergence occurs for initial values not near equilibrium.[12] He has written with Giuseppe Toscani on this subject. WithClément Mouhot, he has worked on nonlinearLandau damping.[16] He has worked on the theory ofoptimal transport and its applications to differential geometry, and withJohn Lott has defined a notion of boundedRicci curvature for general measured length spaces.[17] He also served on the Mathematical Sciences jury for theInfosys Prize in 2015 and 2016.
Villani received the Fields Medal for his work onLandau damping and theBoltzmann equation.[12] He described the development of his theorem in his autobiographical bookThéorème vivant (2012), published inEnglish translation asBirth of a Theorem: A Mathematical Adventure (2015).[18][19] He gave aTED talk at the 2016 conference in Vancouver.[20]
In 2019, Villani applied to be selected to lead the LREM candidate slate forthe 2020 Paris election. By July 2019, he was one of three LREM candidates, alldeputies in theNational Assembly, still seeking the position; the other two wereBenjamin Griveaux (who had been thegovernment spokesperson) andHugues Renson (who had been the vice-president of the National Assembly). On 10 July, the nomination committee picked Griveaux.[25] On 4 September, Villani officially announced his candidacy for the municipal election.[26]
France China Foundation, former Member of the Strategic Committee[27]
In 2018, theFrencheconomicsmagazineChallenges said that Villani has been approached by Europanovathinktank. He presided over the jury of Digital In-Pulse, a startup program dedicated to accompanying entrepreneurs and start-ups, managed byChinesecorporateHuawei. The magazine also says that Villani is still the President of the endowment funds of the FrenchHenri Poincaré Institute, andHuawei is among the top private donors.[28] Villani declined the journalist's request for comment, and the article indicates that the Frenchcounter-intelligence service presented him as "too naïve" regarding those opportunities.
Optimal transportation, dissipative PDE's and functional inequalities, pp. 53–89 inOptimal Transportation and Applications, edited byL. A. Caffarelli and S. Salsa, volume 1813 ofLecture Notes in Mathematics, Springer, 2003,ISBN978-3-540-40192-6.
Les Coulisses de la création, Flammarion, Paris 2015 (with composer and pianistKarol Beffa)
Freedom in Mathematics, Springer India, 2016 (withPierre Cartier, Jean Dhombres, Gerhard Heinzmann),ISBN978-81-322-2786-1. Translation from the French language edition:Mathématiques en liberté, La Ville Brûle, Montreuil 2012,ISBN978-23-601-2026-0.
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,ISBN978-2-36526-252-1.
