Fermat Prize
Encyclopedia
The Fermat prize of mathematical
research
rewards research works in fields where the contributions of Pierre de Fermat
have been decisive:
The spirit of the prize is focused on rewarding the results of researches accessible to the greatest number of professional mathematicians within these fields. The Fermat prize was created in 1989 and is awarded once every two years in Toulouse
by the Institut de Mathématiques de Toulouse
. The amount of the Fermat prize has been fixed at 20,000 Euros for the twelfth edition (2011).
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
research
Research
Research can be defined as the scientific search for knowledge, or as any systematic investigation, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using a scientific method...
rewards research works in fields where the contributions of Pierre de Fermat
Pierre de Fermat
Pierre de Fermat was a French lawyer at the Parlement of Toulouse, France, and an amateur mathematician who is given credit for early developments that led to infinitesimal calculus, including his adequality...
have been decisive:
- Statements of variational principleVariational principleA variational principle is a scientific principle used within the calculus of variations, which develops general methods for finding functions which minimize or maximize the value of quantities that depend upon those functions...
s - Foundations of probabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
and analytic geometryAnalytic geometryAnalytic geometry, or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties... - Number theoryNumber theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
.
The spirit of the prize is focused on rewarding the results of researches accessible to the greatest number of professional mathematicians within these fields. The Fermat prize was created in 1989 and is awarded once every two years in Toulouse
Toulouse
Toulouse is a city in the Haute-Garonne department in southwestern FranceIt lies on the banks of the River Garonne, 590 km away from Paris and half-way between the Atlantic Ocean and the Mediterranean Sea...
by the Institut de Mathématiques de Toulouse
Institut de Mathématiques de Toulouse
The Institut de Mathématiques de Toulouse is the Toulouse Mathematics Institute, a CNRS Research Laboratory which federates the mathematics community of the Toulouse area in France...
. The amount of the Fermat prize has been fixed at 20,000 Euros for the twelfth edition (2011).
Previous prizewinners
- 1989 Awarded jointly to Abbas Bahri for the introduction of new methods in the calculus of variationsCalculus of variationsCalculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
and to Kenneth Ribet for his contribution to number theoryNumber theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
and Fermat's Last TheoremFermat's Last TheoremIn number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
. - 1991 Awarded to Jean-Louis Colliot-ThélèneJean-Louis Colliot-ThélèneJean-Louis Colliot-Thélène is a French mathematician, born on 2 December 1947. He is a Directeur de Recherches at CNRS at the Université Paris-Sud in Orsay.He studies mainly number theory and algebraic geometry with an arithmetic flavor.-Awards:...
for his work on number theoryNumber theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
and rational manifolds the research for which was undertaken to a large extent with J.-J. Sansuc. - 1993 Awarded to Jean-Michel CoronJean-Michel CoronJean-Michel Coron is a French mathematician, born in 1956. He first studied at Ecole Polytechnique where he worked on his PhD thesis advised by Haïm Brezis. Since 1992, his domain of research is the Control Theory of Partial Differential Equations, a domain in which he became a leader, and which...
for his contributions to the study of variational problemsCalculus of variationsCalculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
and control theoryControl theoryControl theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
. - 1995 Awarded to Andrew WilesAndrew WilesSir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory...
for his works on Shimura-Taniyama-Weil's conjecture which resulted in the demonstration of Fermat's Last TheoremFermat's Last TheoremIn number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
. - 1997 Awarded to Michel TalagrandMichel TalagrandMichel Pierre Talagrand is a French mathematician. Docteur ès sciences since 1977, he has been, since 1985, Directeur de Recherches at CNRS and a member of the Functional Analysis Team of the Institut de Mathématique of Paris...
for his fundamental contributions in various domains of probabilityProbability theoryProbability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
. - 1999 Awarded jointly to Fabrice BéthuelFabrice BethuelFabrice Bethuel is a French mathematician. He holds a chair at Paris VI University.Bethuel earned his doctorate at Paris-Sud 11 University in 1989, under supervision of Jean-Michel Coron. He won the 1999 Fermat Prize, jointly with Frédéric Hélein, for several important contributions to the theory...
and Frédéric HéleinFrédéric HéleinFrédéric Hélein is a French mathematician. He holds a chair at Paris Diderot University.Hélein earned his doctorate at École Polytechnique under supervision of Jean-Michel Coron. He won the 1999 Fermat Prize, jointly with Fabrice Bethuel, for several important contributions to the theory of...
for several important contributions to the theory of variational calculus, which have consequences in Physics and Geometry. - 2001 Awarded jointly to Richard TaylorRichard Taylor (mathematician)-External links:**...
for his various contributions to the study of links between Galois representations and automorphic formAutomorphic formIn mathematics, the general notion of automorphic form is the extension to analytic functions, perhaps of several complex variables, of the theory of modular forms...
s and to Wendelin WernerWendelin WernerWendelin Werner is a German-born French mathematician working in the area of self-avoiding random walks, Schramm-Loewner evolution, and related theories in probability theory and mathematical physics. In 2006, at the 25th International Congress of Mathematicians in Madrid, Spain he received the...
for his works on the intersection exponents of Brownian motionBrownian motionBrownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
and their impact in theoretical Physics. - 2003 Awarded to Luigi AmbrosioLuigi AmbrosioLuigi Ambrosio is a professor at Scuola Normale Superiore in Pisa, Italy.His main fields of research are the calculus of variations and geometric measure theory....
(Scuola Normale Superiore, Pisa, Italy) for his impressive contributions to the calculus of variationsCalculus of variationsCalculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
and geometric measure theoryGeometric measure theoryIn mathematics, geometric measure theory is the study of the geometric properties of the measures of sets , including such things as arc lengths and areas. It uses measure theory to generalize differential geometry to surfaces with mild singularities called rectifiable sets...
, and their link with partial differential equationPartial differential equationIn mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s. - 2005 Awarded jointly to Pierre ColmezPierre ColmezPierre Colmez is a French mathematician, notable for his work on p-adic analysis.Colmez studied at Ecole Normale Superieure and obtained his doctorate from Grenoble University. He won the 2005 Fermat Prize for his contributions to the study of L-functions and p-adic Galois representations.Colmez...
for his contributions to the study of L-functionL-functionThe theory of L-functions has become a very substantial, and still largely conjectural, part of contemporary analytic number theory. In it, broad generalisations of the Riemann zeta function and the L-series for a Dirichlet character are constructed, and their general properties, in most cases...
s and p-adic Galois representations and to Jean-François Le GallJean-François Le GallJean-François Le Gall is a French mathematician working in areas of probability theory such as Brownian motion, Lévy processes, superprocesses and their connections with partial differential equations, the Brownian snake, random trees, branching processes, stochastic coalescence and random planar...
for his contributions to the fine analysis of planar Brownian motionBrownian motionBrownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
s, his invention of the Brownian snake and its applications to the study of non-linear partial differential equations. - 2007 Awarded to Chandrashekhar KhareChandrashekhar KhareChandrashekhar B. Khare is a professor of mathematics at the University of California Los Angeles. In 2005, he made a major advance in the field of Galois representations and number theory by proving the level 1 Serre conjecture, and later a proof of the full conjecture with Jean-Pierre Wintenberger...
for his proof (with Jean-Pierre WintenbergerJean-Pierre WintenbergerJean-Pierre Wintenberger is a French mathematician, and currently a professor of mathematics at the University of Strasbourg. He was corecipient of the 2011 Cole Prize in number theory, along with Chandrashekhar Khare, for his proof of Serre's modularity conjecture.Wintenberger earned his Ph.D. at...
) of the Serre modularity conjecture in number theorySerre conjecture (number theory)In mathematics, Jean-Pierre Serre conjectured the following result regarding two-dimensional Galois representations. This was a significant step in number theory, though this was not realised for at least a decade.-Formulation:...
. - 2009 Awarded jointly to Elon LindenstraussElon LindenstraussElon Lindenstrauss is an Israeli mathematician, and a winner of the 2010 Fields Medal.Since 2004, he has been a professor at Princeton University...
for his contributions to ergodic theory and their applications in number theory; and to Cédric VillaniCédric VillaniCédric Villani is a French mathematician working primarily on partial differential equations and mathematical physics. He was awarded the Fields Medal in 2010.-Biography:...
for his contributions to the theory of optimal transport and his studies of non-linear evolution equations. - 2011 Awarded jointly to Manjul BhargavaManjul BhargavaManjul Bhargava is a Canadian-American mathematician of Indian origin. He is the R. Brandon Fradd Professor of Mathematics at Princeton University...
for his work on various generalizations of Davenport-Heilbronn estimates and its recent remarkable results (with Arul Shankar) on the average rank of elliptic curves; and to 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 M. Dafermos, S. Klainerman, H. Lindblad).