Cédric Villani

Cédric Villani (born 5 October 1973) is a French mathematician working primarily on partial differential equations 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 Lyon University. He has been the director of Institut Henri Poincaré in Paris since 2009.^[1][2]

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 fast convergence occurred for initial values not near equilibrium.^[2] He has also written with Giuseppe Toscani on this subject. With Clément Mouhot, he has also worked on nonlinear Landau damping.^[3] 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.^[4]

He received the Fields Medal for his work on Landau damping and the Boltzmann equation.^[2] 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

• Jacques Herbrand Prize (French Academy of Sciences) (2007)
• Prize of the European Mathematical Society (2008)
• Fermat Prize (2009)
• Henri Poincaré Prize (2009)
• Fields Medal (2010)^[2]

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

References

External links

• Cédric Villani's website
• Cédric Villani at the Mathematics Genealogy Project
• Video Interview by ICTP