Cédric Villani

Cédric Villani
Cédric Villani in 2015
Born	5 October 1973 Brive-la-Gaillarde, France[1]
Residence	Paris, France
Nationality	French
Fields	Mathematics
Institutions	Institut Camille Jordan Institut Henri Poincaré University of Lyon
Alma mater	École Normale Supérieure, Paris Dauphine University
Doctoral advisor	Pierre-Louis Lions
Doctoral students	Alessio Figalli Clément Mouhot
Known for	Boltzmann equation Kinetic theory Landau damping Transportation theory Otto–Villani theorem
Notable awards	EMS Prize (2008) Fermat Prize (2009) Henri Poincaré Prize (2009) Fields Medal (2010)
Website cedricvillani.org

Cédric Villani (born 5 October 1973) is a French mathematician working primarily on partial differential equations, Riemannian geometry and mathematical physics. He was awarded the Fields Medal in 2010.

Biography

After attending the Lycée Louis-le-Grand, Villani was admitted at the École normale supérieure in Paris and studied there from 1992 to 1996. He was later appointed an assistant professor in 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 has been the director of Institut Henri Poincaré in Paris since 2009.^[2][3]

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.^[3] He has also written with Giuseppe Toscani on this subject. With Clément Mouhot, he has also worked on nonlinear Landau damping.^[4] 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.^[5]

He received the Fields Medal for his work on Landau damping and the Boltzmann equation.^[3] 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).

Awards and honors

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
• 2006: Institut Universitaire de France
• 2006: Invited lecturer at the International Congress of Mathematicians (Madrid)
• 2007: Jacques Herbrand Prize (French Academy of Sciences)
• 2008: Prize of the European Mathematical Society
• 2009: Henri Poincaré Prize
• 2009: Fermat Prize
• 2010: Fields Medal
• 2013: Gibbs lecturer: On Disorder, Mixing and Equilibration^[6]
• 2014: Joseph L. Doob Prize by the American Mathematical Society for his book Optimal Transport: Old and New (Springer Verlag 2009)^[7]

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^[8]

Selected writings

• Limites hydrodynamiques de l'équation de Boltzmann, Séminaire Bourbaki, June 2001; Astérisque vol. 282, 2002.
• A Review of Mathematical Topics in Collisional Kinetic Theory, in Handbook of Mathematical Fluid Dynamics, edited by S. Friedlander and D. Serre, vol. 1, Elsevier, 2002, ISBN 978-0-444-50330-5. doi:10.1016/S1874-5792(02)80004-0.
• Topics in Optimal Transportation, volume 58 of Graduate Studies in Mathematics, American Mathematical Society, 2003, ISBN 978-0-8218-3312-4.
• 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, ISBN 978-3-540-40192-6.
• 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, ISBN 978-3-540-71049-3.
• Ricci curvature for metric-measure spaces via optimal transport (with John Lott), Annals of Mathematics vol. 169, No. 3 (2009), pp. 903–991.
• Hypocoercivity, volume 202, #950 of Memoirs of the American Mathematical Society, 2009, ISBN 978-0-8218-4498-4.
• Clément Mouhot; Cédric Villani (2009). "On Landau damping". arXiv:0904.2760 [math.AP].
• Théorème vivant, Bernard Grasset, Paris 2012
• Les Coulisses de la création, Flammarion, Paris 2015 (with composer and pianist Karol Beffa)

References

1. Sylvain Guilbaud; Antoine Walraet. "Cédric Villani", Encyclopædia Universalis.
2. Mathematics Genealogy Project – Cédric Villani. Accessed on line 20 August 2010.
3. Fields Medal – Cédric Villani. Accessed on line 20 August 2010
4. Clément Mouhot; Cédric Villani (2010). "Landau damping". Journal of Mathematical Physics 51 (15204): 015204. arXiv:0905.2167. doi:10.1063/1.3285283.
5. John Lott; Cedric Villani (2004). "Ricci curvature for metric-measure spaces via optimal transport". arXiv:math/0412127 [math.DG].
6. Josiah Willard Gibbs Lectures - No. 86, January 2013, San Diego, CA; Cédric Villani Accessed on line 20 May 2015.
7. Joseph L. Doob Prize - Most Recent Prize: 2014 Accessed on line 20 May 2015.
8. Cédric Villani, new member of the French Academy of Science Accessed on line 20 May 2015.

External links

• Cédric Villani's website
• Cédric Villani at the Mathematics Genealogy Project
• Video Interview by ICTP
• Review of 'Birth of a Theorem'