Villani has given two lectures at the Royal Institution, the first titled 'Birth of a Theorem'.[2] 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 the one 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'.[3]
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 winning mathematician John F. Nash, Jr.[13]
Several months later, on 23 May 2015, Nash, along with his wife, Alicia died in a car crash. Speaking at the Hay Festival, 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.[14]
Mathematical work
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.[11] He has written with Giuseppe Toscani on this subject. With Clément Mouhot, he has worked on nonlinear Landau damping.[15] 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.[16] 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.[11] 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).[17][18] He gave a TED talk at the 2016 conference in Vancouver.[19]
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 theNational 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.[24] On 4 September, Villani officially announced his candidacy for the municipal election.[25]
Other activities
France China Foundation, former Member of the Strategic Committee[26]
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)[27]
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, ISBN978-3-540-40192-6.
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, ISBN978-3-540-71049-3.
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), 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.