# Fermat Prize of the Université Paul Sabatier

The

**Fermat Prize**is awarded to a mathematician for decisive research in those fields to which Pierre de Fermat contributed, namely: Statements of Variational Principles; Foundations of Probability and Analytical Geometry; and Number Theory. The main aim is to reward those whose researches are accessible to the greatest number of professional mathematicians within these fields.**1989**A Bahri... for the introduction of new methods in the Calculation of Variations.

**1989**K A Ribet... for his contribution to Number Theory and Fermat's last Theorem.

**1991**J-L Colliot-Thélène... for his work on Number Theory and rational manifolds the research for which was undertaken to a large extent with J-J Sansuc.

**1993**J-M Coron... for his contributions to the study of Variational Problems and Control Theory.

**1995**A J Wiles... for his works on Shimura-Taniyama-Weil's conjecture which resulted in the demonstration of Fermat's Last Theorem.

**1997**M Talagrand... for his fundamental contributions in various domains of Probability.

**1999**F Bethuel and F Helein... for several important contributions to the theory of variational calculus, which have consequences in Physics and Geometry.

**2001**R L Taylor... for his various contributions to the study of links between Galois representations and automorphic forms.

**2001**W Werner... for his works on the intersection exponents of Brownian motion and their impact in theoretical Physics.

**2003**L Ambrosio... for his impressive contributions to the Calculus of Variations and Geometric Measure Theory, and their link with partial differential equations.

**2005**P Colmez... for his contributions to the study of L functions and p-adic Galois representations.

**2005**J-F Le Gall... for his contributions to the fine analysis of planar Brownian motions, his invention of the Brownian snake and its applications to the study of non-linear partial differential equations.

**2007**C Khare... for his proof, in collaboration with Jean-Pierre Wintenberger, of Serre's modularity conjecture in number theory.

**2009**Elon Lindenstrauss... for his contributions to ergodic theory and their applications in number theoryCédric Villani

... for his contributions to the theory of optimal transport and his studies of non-linear evolution equations.

**2011**Manjul Bhargava... for his work on various generalizations of the Davenport-Heilbronn estimates and for his recent startling results (with Arul Shankar) on the average rank of elliptic curves;Igor Rodnianski

... for his fundamental contributions to the studies of the equations of general relativity and to the propagation of the light on the space-time curves (in collaboration with Mihalis Dafermos, Sergiu Klainerman, and Hans Lindblad).

**2013**Camillo De Lellis... for his fundamental contributions (in collaboration with László Székelyhidi) to the conjecture of Onsager about dissipative solutions of the Euler-equations and for his work to the regularity of minimal surfaces;Martin Hairer

... for his contributions to the analysis of stochastic partial differential equations, especially for the regularity of their solutions and convergence to the equilibrium.

**2015**Laure Saint-Raymond... for the development of asymptotic theories of partial differential equations, including the fluid limits of rarefied flows, multiscale analysis in plasma physics equations and ocean modeling, and the derivation of the Boltzmann equation from interacting particle systems;Peter Scholze

... for his invention of perfectoid spaces and their application to fundamental problems in algebraic geometry and in the theory of automorphic forms.

**2017**Simon Brendle... for his numerous and profound results in geometric analysis, involving partial differential equations of elliptic, parabolic and hyperbolic type; in particular for his elegant proof of Lawson's conjecture, for his characterization of soliton solutions of Ricci flows and mean curvature in dimension 3 as well as for his remarkable contributions, in collaboration with Gerhard Huisken, to the analysis of mean curvature flow of mean convex surfaces in manifolds of dimension 3;Nader Masmoudi

... for his remarkable work of depth and creativity in the analysis of nonlinear partial differential equations and in particular for his recent contributions to the rigorous and complete resolution of hydrodynamic stability problems raised at the end of the 19th century by the founding fathers of modern fluid mechanics.

**2019**Alexei Borodin... for the invention of integrable probability theory, a new area at the interface of representation theory, combinatorics and statistical physics;Maryna Viazovska

... for her original solution of the famous sphere packing problem in dimensions 8 and 24.