Cédric Villani

Cédric Villani 2015

Cédric Villani (born October 5, 1973 in Brive-la-Gaillarde ) is a multiple award-winning (inter alia Fields Medal 2010) French mathematical physicist and mathematician and politician .

life and work

Villani studied from 1992 at the École Normale Supérieure . In 1994 he acquired his Agrégation . In 1998 he did his PhD with Pierre-Louis Lions . Villani has been a professor at the École normal supérieure de Lyon since 2001 . Since 2009 he has been director of the Institut Henri Poincaré in Paris . Since 2007 he has been a member of the Institut Universitaire de France.

Villani deals in particular with partial differential equations from statistical mechanics , especially the Boltzmann equation , where he was the first to prove convergence theorems for initial values ​​not close to equilibrium. These are quantitative versions (rate of relaxation towards equilibrium) of Ludwig Boltzmann's H-theorem . He also dealt with applications of the theory of optimal transport (the theory goes back to a question posed by Monge and was developed in particular by Kantorowitsch ) in differential geometry - in particular, with its help, he gave lower bounds of the Ricci curvature in general metric with John Lott Spaces ( length spaces ).

He received the Fields Medal primarily for his work on the Boltzmann equation and the nonlinear Landau damping from the kinetic equations of plasma physics (Vlasov equation). This corresponds to the mathematically very different cases of kinetic equations with collision (Boltzmann equation) and without collision (plasma physics with Coulomb repulsion, astrophysics, for example, of stars in galaxies with attractive gravitational interaction). In the case without a collision, he was able to justify the Landau damping in the non-linear perturbative case. The solution also showed unexpected connections to the KAM theory and the phenomenon of the plasma echo and highlighted the special role of the regularity assumptions (the proof was given for Gevrey regularity and for the periodic case). The non-perturbation theory case ( violent relaxation ) is less well understood. The case of the Boltzmann equation with collision is different, here the entropy production plays a central role in approaching equilibrium. Villani proved, among other things, a conjecture by Cercignani, according to which the entropy production is at least proportional to the difference between the entropy of the velocity distribution and that of the Gaussian distribution. He reported on the genesis of his research in the book "The living theorem" ( Théorème vivant , 2012), which was published in 2013 in German translation.

In February 2018, he submitted a comprehensive report (21 mesures pour l'enseignement des mathématiques, prepared under the direction of himself and Charles Torossian ) to the French Ministry of Education on the reform of French mathematics teaching. In March 2018, he presented the report AI for humanity for the promotion of artificial intelligence (AI), the preparation of which he had previously been commissioned by the official French side. The text, also known as the Villani Report , is considered a French AI strategy .

His PhD students include Alessio Figalli and Clément Mouhot .

Political career

Villani at a meeting of La République en Marche in Tokyo

In 2015 the European Commission appointed him to the seven-member "High Level Group of Scientific Advisors". In 2016 he was made a full member of the Pontifical Academy of Sciences .

Villani supported the election of the first woman mayor of Paris, Anne Hidalgo . In the parliamentary elections in France in 2017 , Cedric Villani was elected Member of the National Assembly for the party La République en Marche in the 5th constituency of the Essonne department .

In 2019, he announced his candidacy for the Mayor of Paris in spring 2020, in competition with the candidate of his party La République en Marche (LREM), Benjamin Griveaux . After Griveaux's withdrawal in February 2020, talks began between his successor candidate Agnès Buzyn and Villani about conditions for a merger of the two candidacies. In January 2020 he was expelled from the LREM and joined the group of ex-members of the LREM in the Parliament Écologie démocratie solidarité (EDS) founded in May .

See also : List of members of the National Assembly of the 15th electoral term (France)

Awards and honors

In 2010 he received the Fields Medal . In 2009 he received the Henri Poincaré Prize for innovative work on kinetic theory and optimal transport with applications to dissipative physical systems and Riemannian geometry . Also in 2009 he received the Fermat Prize and in 2008 the EMS Prize . In 2007 he received the Prix ​​Jacques Herbrand of the French Mathematical Society, in 2003 the Peccot Vimont Prize of the Collège de France and in 2001 the Louis Armand Prize of the French Academy of Sciences. In 2006 he was invited speaker at the International Congress of Mathematicians (ICM) in Madrid (Hypocoercive diffusion operators) and in 2003 he was plenary speaker at the International Congress for Mathematical Physics. Since 2012 he has been a member of the Academia Europaea and an honorary member of the Royal Irish Academy . In 2013 he was elected to the Académie des Sciences . Also in 2013 he was Gibbs Lecturer and in 2014 he received the Joseph L. Doob Prize (for his book Optimal Transport ). In 2011 he became a Knight of the Legion of Honor . In 2013/14 and 2014/15 he was on the Abel Prize Committee. In 2017 Villani gave a Gauss lecture ( On triangles, gases, prices and men ).

The newly discovered species of spider Araniella villanii from the Araneidae family , which weaves architecturally sophisticated and aesthetically pleasing webs that look like they are implementing the golden section , was named after him in 2020. The spider is light green and lives, among other things, in bushes and forests in northern India , southwest Iran and eastern Kazakhstan . Villani has a penchant for spiders and often wears a spider- shaped brooch .

Fonts

• with Giuseppe Toscani: Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation. In: Communications in Mathematical Physics . Vol. 203, No. 3, 1999, pp. 667-706, doi : 10.1007 / s002200050631 .
• with Giuseppe Toscani: On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds. In: Journal of Statistical Physics. Vol. 98, No. 5/6, 2000, pp. 1279-1309, doi : 10.1023 / A: 1018623930325 .
• Limites hydrodynamiques de l'équation de Boltzmann (d'après C. Bardos, F. Golse, CD Levermore, P.-L. Lions, N. Masmoudi, L. Saint-Raymond). In: Séminaire Bourbaki . Année 53, No. 893, 2000/2001 = Astérisque. Vol. 282, 2002, pp. 365-405, ( digitized version ).
• A Review of Mathematical Topics in collisional kinetic theory. In: Denis Serre , Susan Friedlander (Eds.): Handbook of mathematical fluid dynamics. Volume 1. Elsevier, Amsterdam et al. 2002, ISBN 0-444-50330-7 , pp. 71-305.
• Cercignani's conjecture is sometimes true and always almost true. In: Communications in Mathematical Physics. Vol. 234, No. 3, 2003, pp. 455-490, doi : 10.1007 / s00220-002-0777-1 .
• Optimal transportation, dissipative PDEs and functional inequalities. In: Luis A. Caffarelli , Sandro Salsa (Ed.): Optimal transportation and applications. Lectures given at the CIME summer school held in Martina Franca, Italy, September 2–8, 2001 (= Lecture Notes in Mathematics . 1813). Springer, Berlin et al. 2003, ISBN 3-540-40192-X , pp. 53-89.
• Topics in Optimal Transportation (= Graduate Studies in Mathematics. 58). American Mathematical Society, Providence RI 2003, ISBN 0-8218-3312-X .
• with Laurent Desvillettes: On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation. In: Inventiones Mathematicae . Vol. 159, No. 2, 2005, pp. 245-316, doi : 10.1007 / s00222-004-0389-9 .
• Mathematics of granular materials. In: Journal of Statistical Physics. Vol. 124, No. 2/4, 2006, pp. 781-822, doi : 10.1007 / s10955-006-9038-6 .
• Hypocoercivity (= Memoirs of the American Mathematical Society. 950). American Mathematical Society, Providence RI 2009, ISBN 978-0-8218-4498-4 .
• Optimal transport. Old and new (= basic teachings of the mathematical sciences . 338). Springer, Berlin et al. 2009, ISBN 978-3-540-71049-3 .
• with Clément Mouhot : On Landau damping. In: Acta Mathematica . Vol. 207, No. 1, 2011, pp. 29-201, Arxiv .
• with Pierre Cartier , Jean Dhombres , Gerhard Heinzmann : Mathématiques en liberté. La ville brûle, Montreuil (Seine-Saint-Denis) 2012, ISBN 978-2-36012-026-0 (English: Freedom in Mathematics. Springer India, New Delhi 2016, ISBN 978-81-322-2786-1 ; also as: Conversation sur les mathématiques. Flammarion, Paris 2019, ISBN 978-2-0814-7873-2 ).
• Théorème vivant. Grasset, Paris 2012, ISBN 978-2-253-17490-5 (Review by Jacques Hurtubise in: Notices of the American Mathematical Society. Vol. 61, No. 2, 2014, pp. 172-173 ; German translation: Das lebige Theorem. S. Fischer, Frankfurt am Main 2013, ISBN 978-3-10-086007-1 ).
• with Karol Beffa: Les Coulisses de la création. Flammarion, Paris 2015, ISBN 978-2-0813-6070-9 (with composer and pianist Karol Beffa).

Web links

Commons : Cédric Villani  - collection of images, videos and audio files

• Homepage
• The mathematician with the spider brooch , ZEIT Online, August 18, 2010 (on the Fields Medal 2010)
• Felix Otto : A Fields Medal for Cedric Villani (PDF file; 236 kB), messages from the DMV
• Christoph Drösser : Cédric Villani: On the scholar's shoulder , ZEIT Online, April 25, 2013
• Nothing works without luck , Arno Widmann : Interview with Cédric Villani, Berliner Zeitung, May 21, 2013
• Villani on his research , Quora
• Videos by and about Cédric Villani in the AV portal of the Technical Information Library

References

1. ^ Villani, John Lott : Ricci Curvature for metric-measure spaces via optimal transport. In: Annals of Mathematics . Vol. 169, No. 3, 2009, pp. 903-991, JSTOR 25662148 .
2. ^ Ilka Agricola : 21 mesures pour l'enseignement des mathématiques / The Villani-Torossian report on mathematics teaching in France. In: Communications of the German Mathematicians Association . Vol. 26, No. 2/3, 2018, pp. 121–124, doi : 10.1515 / dmvm-2018-0033 .
3. ↑ 21 mesures pour l'enseignement des mathématiques
4. ^ AI for humanity
5. ↑ Marie de Chalup: Artificial Intelligence. Key points on the French AI strategy. In: idw - Information Service Science. French Embassy in the Federal Republic of Germany. Scientific Department, April 24, 2018, accessed September 17, 2019 . 
6. ^ Nomina di Membri Ordinari della Pontificia Accademia delle Scienze. In: Daily Bulletin. Holy See Press Office , June 24, 2016, accessed June 24, 2016 (Italian). 
7. ↑ le génie des maths Cédric Villani explique pourquoi il est candidat de la République en marche aux législatives (French)
8. ^ Législatives en Ile-de-France: En Marché et le MoDem en tête dans 86% des circonscriptions ( French ) Le Parisien . June 12, 2017. Accessed on June 12, 2017: “Le meilleur score est obtenu par le mathématicien Cédric Villani qui obtient 47.5% des voix dans la 5e circonscription.”
9. ↑ Official election result of both ballots ( French ) Frz. Home Office. June 18, 2017. Retrieved June 18, 2017.
10. ↑ Der Spiegel , No. 37, 2019, p. 77
11. ↑ Mathilde SIRAUD: Municipales à Paris: Agnès Buzyn et Cédric Villani se sont entretenus par téléphone .
12. ^ Theory of the Boltzmann equation
13. ↑ Appreciation for the Poincaré Prize, innovative work on kinetic theory and optimal transport with applications to dissipative physical systems and Riemannian geometry.
14. ↑ Laura Geggel, Newly discovered neon-green spider named after the "Lady Gaga of mathematics" , Live Science 2020