Professor, Collège de France and École Polytechnique
Pierre-Louis Lions is one of the most well known mathematicians of our time. He graduated from the École Normale Supérieure in 1977, and received his doctorate from the University of Pierre and Marie Curie in 1979.
His main work is on the theory of nonlinear partial differential equations. He received the Fields Medal (comparable to a Nobel Prize) for his work in 1994. Lions was the first to give a complete solution to the Boltzmann equation with proof. He has received numerous other awards. Currently, he holds the position of Professor of Partial differential equations and their applications at the prestigious Collège de France in Paris as well as a position at Ecole Polytechnique.
In the paper “Viscosity solutions of Hamilton-Jacobi equations” (1983), written with Michael Crandall, he introduced the notion of viscosity solutions. This has had a great effect on the theory of partial differential equations. More recent work includes the theory of mean-field games, which promises to be highly influential in economics.
Pierre-Louis Lions has also been interested for a long time in mathematical finance writing seminal papers on a variety of subjects, such as the use of Malliavin calculus, Monte Carlo methods, applications of stochastic control, and convexity properties.
http://en.wikipedia.org/wiki/Pierre-Louis_Lions (in English)
http://www.college-de-france.fr/default/EN/all/equ_der/biographie.htm (in French)
Mathematics Genealogy, including graduated PhD students