Pierre-Louis Lions

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Pierre-Louis Lions
Pierre-Louis Lions par Philippe Binant.jpg
Pierre-Louis Lions
Born (1956-08-11) 11 August 1956 (age 62)
Alma materÉcole normale supérieure
Pierre and Marie Curie University
Known forNonlinear partial differential equations
Mean field game theory
AwardsFields Medal (1994)
Scientific career
InstitutionsCollège de France
École Polytechnique
University of Paris-Dauphine
ThesisSur quelques classes d'équations aux dérivees partielles non linéaires et leur résolution numérique (1979)
Doctoral advisorHaïm Brezis
Doctoral studentsOlivier Guéant
Gilles Motet
Cédric Villani

Pierre-Louis Lions (French: [ljɔ̃ːs];[1] born 11 August 1956) is a French mathematician. He is the recipient of the 1994 Fields Medal.


His parents were Jacques-Louis Lions, a mathematician and at that time professor at the University of Nancy, who became President of the International Mathematical Union, and Andrée Olivier, his wife. He graduated from the École normale supérieure in 1977 (same year as Jean-Christophe Yoccoz, another Fields Medalist). Refusing to take the agrégation in Mathematics, he chose to carry out research in applied mathematics and received his doctorate from the University of Pierre and Marie Curie in 1979.[2]

Lions received the Fields Medal, for his work on theory of nonlinear partial differential equations, in 1994 while working at the University of Paris-Dauphine. He was the first to give a complete solution to the Boltzmann equation with proof. Other awards Lions received include the IBM Prize in 1987 and the Philip Morris Prize in 1991. He was an invited professor at the Conservatoire national des arts et métiers (2000).[3] He is a doctor honoris causa of Heriot-Watt University[4] (Edinburgh), Narvik University College (2014), and of the City University of Hong-Kong and is listed as an ISI highly cited researcher.[5] He holds the position of Professor of Partial differential equations and their applications at the Collège de France in Paris as well as a position at École Polytechnique.

In the paper "Viscosity solutions of Hamilton-Jacobi equations" (1983), written with Michael G. Crandall, he introduced the notion of viscosity solutions. This has had an effect on the theory of partial differential equations.


  • Lions, P. L.; Lasry, J. M. (2007). "Large investor trading impacts on volatility". Annales de l'Institut Henri Poincaré C. 24 (2): 311. doi:10.1016/j.anihpc.2005.12.006.
  • Lasry, J. M.; Lions, P. L. (2007). "Mean field games". Japanese Journal of Mathematics. 2: 229. doi:10.1007/s11537-007-0657-8.
  • Lasry, J. M.; Lions, P. L. (2006). "Jeux à champ moyen. II – Horizon fini et contrôle optimal". Comptes Rendus Mathématique. 343 (10): 679. doi:10.1016/j.crma.2006.09.018.
  • Lasry, J. M.; Lions, P. L. (2006). "Jeux à champ moyen. I – Le cas stationnaire". Comptes Rendus Mathématique. 343 (9): 619. doi:10.1016/j.crma.2006.09.019.
  • Pierre-Louis Lions, Equations aux dérivées partielles et applications, Cours et travaux du Collège de France, Paris, 2002-2015.


  1. ^ CORE Fields Medal Talk: Pierre-Louis Lions on Mean Field Games
  2. ^ "La Médaille Fields : 11 lauréats sur 44 sont issus de laboratoires français., Alain Connes," (PDF). www2.cnrs.fr. Retrieved 11 May 2010.
  3. ^ Pierre-Louis Lions, « Analyse, modèles et simulations », Université de tous les savoirs, 4, 86-92, Éditions Odile Jacob, Paris, 2001.
  4. ^ Hoffmann, Ilire Hasani, Robert. "Academy of Europe: Lions Pierre-Louis". www.ae-info.org. Retrieved 2016-04-06.
  5. ^ Thomson ISI, Lions, Pierre-Louis, ISI Highly Cited Researchers, archived from the original on 2006-03-04, retrieved 2009-06-20

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