Cédric Villani
fl. 1973, Brive-la-Gaillarde, France
AnalysisDifferential equations and dynamical systemsApplied and computational mathematicsFields Medal 2010
French mathematician who proved major regularity and convergence results for the Boltzmann equation and developed modern optimal-transport methods.
Cédric Villani studied nonlinear partial differential equations, kinetic theory, and optimal transport. His work on the Boltzmann equation explains how collisions drive systems toward equilibrium, while his collaboration with Félix Otto developed powerful links between transport geometry and diffusion. He received the 2010 Fields Medal.
Workplaces: University of Lyon
France
Award-winning work
Fields Medal 2010Awarded for his work on nonlinear Landau damping, the Boltzmann equation, and optimal transport. Villani proved rigorous convergence and regularity results for the Boltzmann equation of kinetic theory, and with Clément Mouhot he proved that Landau damping — the attenuation of plasma oscillations predicted on physical grounds by Landau — really occurs for nonlinear perturbations of the Vlasov equation. He also reshaped the theory of optimal transport, linking the geometry of Ricci curvature to the transport of measures. His monograph Optimal Transport: Old and New became the standard reference and spread these methods across analysis, geometry, and probability.