Cédric Villani

2.1. Early Life and Education

Villani was born on 5 October 1973, in Brive-la-Gaillarde, Corrèze, France. He attended the renowned Lycée Louis-le-Grand before being admitted to the École Normale Supérieure in Paris. He studied there from 1992 to 1996, after which he was appointed an agrégé préparateur, a type of assistant professor, at the same institution.

2.2. Academic Career

Cédric Villani pursued his doctoral studies at Paris Dauphine University, completing his PhD in 1998 under the supervision of Pierre-Louis Lions, a fellow Fields Medalist. Following his doctorate, he became a professor at the École normale supérieure de Lyon in 2000. He currently holds a professorship at the University of Lyon and, as of September 2022, is also a professor at the Institut des Hautes Études Scientifiques (IHES). From 2009 to 2017, Villani served as the director of the Institut Henri Poincaré in Paris. His academic career has also included several visiting positions at notable institutions, such as Georgia Tech in the Fall of 1999, the University of California, Berkeley in the Spring of 2004, and the Institute for Advanced Study in Princeton in the Spring of 2009. Villani is fluent in French, English, and Italian.

On 19 October 2014, Villani participated in a conversation with Nobel Prize-winning mathematician John Forbes Nash Jr. as part of the inaugural Albertine festival hosted by the Cultural Services of the French Embassy. Several months later, on 23 May 2015, Nash and his wife, Alicia, tragically died in a car crash. Speaking at the Hay Festival just days after Nash's death, Villani revealed that Nash had told him in Norway on 20 May that he had discovered a "replacement equation" for Einstein's theory of relativity.

3.1. Research Areas

Villani's primary research areas include the theory of partial differential equations, particularly those involved in statistical mechanics. He has extensively studied the Boltzmann equation, where he, along with Laurent Desvillettes, was the first to prove the rate of convergence for initial values not near equilibrium. He has also collaborated with Giuseppe Toscani on this subject. His work with Clément Mouhot focused on nonlinear Landau damping. Additionally, Villani has made significant contributions to the theory of optimal transport and its applications to differential geometry. In collaboration with John Lott, he defined a notion of bounded Ricci curvature for general measured length spaces.

3.2. Key Contributions

Among Villani's specific mathematical achievements is his work proving Cercignani's conjecture, which he described in his autobiographical book Théorème vivant (Living Theorem). A particularly notable accomplishment is the "Mouhot-Cédric Theorem," which he completed in December 2009 with his colleague Clément Mouhot. This theorem addressed the regularity problem of inhomogeneous Boltzmann equations and mathematically substantiated Lev Davidovich Landau's concept of Landau damping, a phenomenon in plasma physics first proposed by Landau, a Nobel Prize laureate in Physics in 1962.

3.3. Fields Medal Award

In 2010, Cédric Villani was awarded the prestigious Fields Medal, often regarded as the Nobel Prize of mathematics. The award recognized his profound work on Landau damping and the Boltzmann equation. He received the medal at the International Congress of Mathematicians (ICM) held in 2010, alongside fellow mathematicians Elon Lindenstrauss, Ngô Bảo Châu, and Stanislav Smirnov. Villani detailed the development of his theorem in his autobiographical book Théorème vivant (2012), which was later published in English translation as Birth of a Theorem: A Mathematical Adventure (2015).

3.4. Other Academic Recognition

Beyond the Fields Medal, Villani has received numerous other academic distinctions. He has been a plenary lecturer at major international conferences, including the International Congress of Mathematical Physics in Lisbonne in 2003 and an invited lecturer at the International Congress of Mathematicians in Madrid in 2006. He also delivered a TED talk titled "What's so sexy about math?" at the 2016 conference in Vancouver. Villani has given two lectures at the Royal Institution in London: "Birth of a Theorem" on 22 April 2015, which shares its title with the English translation of his book, and "The Extraordinary Theorems of John Nash" on 2 November 2016. He also served on the Mathematical Sciences jury for the Infosys Prize in 2015 and 2016.

4.1. Entry into Politics and Election

In 2017, Villani was selected as a candidate for La République En Marche! (LREM), the political party founded by Emmanuel Macron, to contest the Essonne's 5th constituency in the 2017 French legislative election. In the first round of voting, Villani secured 47% of the votes, positioning him strongly for the second round. He subsequently won the second round with 69.36% of the vote, becoming a deputy in the National Assembly, the lower house of the French Parliament. He served in this role from 21 June 2017 to 21 June 2022, succeeding Maud Olivier and being succeeded by Paul Midy.

4.2. Party Affiliations and Political Stances

Initially elected as a member of La République En Marche! (LREM), Villani's political affiliations evolved. In May 2020, he left LREM to co-found a new parliamentary group, Ecology, Democracy, Solidarity (EDS). Following the dissolution of EDS, Villani joined Ecology Generation. For the 2022 French legislative election, he ran for re-election under the banner of the NUPES (Nouvelle Union Populaire écologique et sociale), a broad left-wing and green political coalition. His decision to run for the 2020 Paris municipal election against the official LREM candidate led to his expulsion from the ruling party.

4.3. Parliamentary Role and Activities

As a Member of Parliament, Villani took on significant responsibilities. In July 2017, he was elected as the Vice President of the French Parliamentary Office for the Evaluation of Scientific and Technological Choices. This role allowed him to leverage his scientific expertise in legislative discussions and policy-making related to science and technology.

4.4. Electoral Campaigns

Villani's political ambitions extended to local elections. In 2019, he sought to lead the LREM candidate slate for the 2020 French municipal elections in Paris. By July 2019, he was one of three LREM deputies vying for the position, alongside Benjamin Griveaux and Hugues Renson. However, the party's nomination committee ultimately chose Griveaux on 10 July. Despite this, Villani officially announced his independent candidacy for the Paris municipal election on 4 September 2019. In the 2022 French legislative election, he sought re-election but lost his seat to La République En Marche! candidate Paul Midy by a narrow margin of 19 votes.

6.1. Academic Awards

In addition to the prestigious Fields Medal received in 2010, Villani's academic accolades include:

• 1998**: PhD Thesis (under P.-L. Lions)
• 2000**: Habilitation dissertation
• 2001**: Louis Armand Prize of the French Academy of Sciences
• 2003**: Peccot-Vimont Prize and Cours Peccot of the Collège de France
• 2004**: Harold Grad lecturer
• 2004**: Visiting Miller Professor, University of California, Berkeley
• 2006**: Institut Universitaire de France
• 2007**: Grand Prix Jacques Herbrand of the French Academy of Sciences
• 2008**: Prize of the European Mathematical Society
• 2009**: Henri Poincaré Prize
• 2009**: Fermat Prize
• 2013**: Gibbs lecturer for "On Disorder, Mixing and Equilibration"
• 2014**: Joseph L. Doob Prize by the American Mathematical Society for his book Optimal Transport: Old and New (Springer Verlag 2009)
• 2014**: Pius XI Medal

6.2. Other Social Honors

Beyond his academic achievements, Villani has been recognized with several extra-academic distinctions:

• 2009**: Knight of the National Order of Merit (France)
• 2011**: Knight of the Legion of Honor
• 2013**: Member of the French Academy of Sciences
• 2016**: Ordinary member of the Pontifical Academy of Sciences
• 2022**: Fellow of the International Science Council