- Definições em cálculo de variações
- Fundamentos da probabilidade e geometria analítica
- Teoria dos números.
O espírito norteador do prêmio é focado na recompensa dos resultados de pesquisas acessíveis ao maior número de matemáticos profissionais nas três áreas acima. O Prêmio Fermat foi criado em 1989 e é concedido a cada dois anos em Toulouse pelo Institut de Mathématiques de Toulouse. Foi dotado em 20 000 Euros para a décima primeira edição (2009).
- 1989 Awarded jointly to Abbas Bahri for the introduction of new methods in the calculus of variations and to Kenneth Ribet for his contribution to number theory and Fermat's Last Theorem.
- 1991 Awarded to Jean-Louis 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 Awarded to Jean-Michel Coron for his contributions to the study of variational problems and control theory.
- 1995 Awarded to Andrew Wiles for his works on Shimura-Taniyama-Weil's conjecture which resulted in the demonstration of Fermat's Last Theorem.
- 1997 Awarded to Michel Talagrand for his fundamental contributions in various domains of probability.
- 1999 Awarded jointly to Fabrice Béthuel and Frédéric Hélein for several important contributions to the theory of variational calculus, which have consequences in Physics and Geometry.
- 2001 Awarded jointly to Richard Taylor for his various contributions to the study of links between Galois representations and automorphic forms and to Wendelin Werner for his works on the intersection exponents of Brownian motion and their impact in theoretical Physics.
- 2003 Awarded to Luigi Ambrosio (Scuola Normale Superiore, Pisa, Italie) for his impressive contributions to the calculus of variations and geometric measure theory, and their link with partial differential equations.
- 2005 Awarded jointly to Pierre Colmez for his contributions to the study of L-functions and p-adic Galois representations and to Jean-François 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 Awarded to Chandrashekhar Khare for his proof with Jean-Pierre Wintenberger of the Serre modularity conjecture in number theory.
- 2009 Awarded jointly to Elon Lindenstrauss for his contributions to ergodic theory and their applications in number theory; and to Cédric Villani for his contributions to the theory of optimal transport and his studies of non-linear evolution equations.
Prêmio Fermat Junior [editar]
The Junior Fermat Prize is a mathematical prize, awarded every two years to a student in the first three years of university for a contribution to mathematics. The amount of the prize is 2000 Euros.