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Fermat Prize
The Fermat prize of mathematics, mathematical research biennially rewards research works in fields where the contributions of Pierre de Fermat have been decisive: * Statements of variational principles * Foundations of probability and analytic geometry * Number theory. The spirit of the prize is focused on rewarding the results of research 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). Previous prize winners Pierre Fermat medal There has also been a ''Pierre Fermat medal'', which has been awarded for example to chemist Linus Pauling (1957), mathematician Ernst Peschl (1965) and botanist Francis Raymond Fosberg. Junior Fermat Prize The Junior Fermat Prize is a mathematical prize, awarded every two years to a stud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Michel Coron
Jean-Michel Coron (born August 8, 1956) is a French mathematician. He first studied at École Polytechnique, where he worked on his PhD thesis advised by Haïm Brezis. Since 1992, he has studied the control theory of partial differential equations, and which includes both control and stabilization. His results concern partial differential equations related to fluid dynamics, with emphasis on nonlinear phenomena, and part of them found applications to control channels. He had previously worked in the field of non-linear functional analysis, where he also obtained significant results. Jean-Michel Coron was awarded numerous prizes, such as the Fermat prize in 1993, the Peccot lecture in 1987, the Jaffé prize in 1995 by the Académie des Sciences, and the Dargelos prize in 2002. He was invited at the 1990 International Congress of Mathematicians (Kyoto) in the section Partial Differential Equations, and he was also invited as a plenary speaker at the 2010 International Con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brownian Motion
Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). The traditional mathematical formulation of Brownian motion is that of the Wiener process, which is often called Brownian motion, even in mathematical sources. This motion pattern typically consists of Randomness, random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such a fluid, there exists no preferential direction of flow (as in transport phenomena). More specifically, the fluid's overall Linear momentum, linear and Angular momentum, angular momenta remain null over time. The Kinetic energy, kinetic energies of the molecular Brownian motions, together with those of molecular rotations and vibrations, sum up to the caloric component of a fluid's in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wendelin Werner
Wendelin Werner (born 23 September 1968) is a German-born French mathematician working on random processes such as self-avoiding random walks, Brownian motion, 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 Fields Medal "for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory". He is currently Rouse Ball professor of Mathematics at the University of Cambridge. Biography Werner was born on 23 September 1968 in Cologne, West Germany. His parents moved to France when he was nine months old and he became a French citizen in 1977. After a '' classe préparatoire'' at Lycée Hoche in Versailles, he studied at École Normale Supérieure from 1987 to 1991. His 1993 doctorate was written at the Université Pierre-et-Marie-Curie and supervised by Je ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automorphic Form
In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular forms are holomorphic automorphic forms defined over the groups SL(2, R) or PSL(2, R) with the discrete subgroup being the modular group, or one of its congruence subgroups; in this sense the theory of automorphic forms is an extension of the theory of modular forms. More generally, one can use the adelic approach as a way of dealing with the whole family of congruence subgroups at once. From this point of view, an automorphic form over the group ''G''(A''F''), for an algebraic group ''G'' and an algebraic number field ''F'', is a complex-valued function on ''G''(A''F'') that is l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galois Representations
In mathematics, a Galois module is a ''G''-module, with ''G'' being the Galois group of some extension of fields. The term Galois representation is frequently used when the ''G''-module is a vector space over a field or a free module over a ring in representation theory, but can also be used as a synonym for ''G''-module. The study of Galois modules for extensions of local or global fields and their group cohomology is an important tool in number theory. Examples *Given a field ''K'', the multiplicative group (''Ks'')× of a separable closure of ''K'' is a Galois module for the absolute Galois group. Its second cohomology group is isomorphic to the Brauer group of ''K'' (by Hilbert's theorem 90, its first cohomology group is zero). *If ''X'' is a smooth proper scheme over a field ''K'' then the ℓ-adic cohomology groups of its geometric fibre are Galois modules for the absolute Galois group of ''K''. Ramification theory Let ''K'' be a valued field (with valuation denoted '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Taylor (mathematician)
Richard Lawrence Taylor (born 19 May 1962) is a British mathematician working in the field of number theory. He is currently the Barbara Kimball Browning Professor in Humanities and Sciences at Stanford University in California. Taylor received the 2002 Cole Prize, the 2007 Shaw Prize with Robert Langlands, and the 2015 Breakthrough Prize in Mathematics. Career He received his B.A. from Clare College, Cambridge.SAVILIAN PROFESSORSHIP OF GEOMETRY in NOTICES, University Gazette 23.3.95 No. 435 During his time at University of Cambridge, Cambridge, he was president of The Archimedeans in 1981 and 1982, following the resignation of his predecessor. He earned his Ph.D. in mathematics from Princeton University in 1988 after completing a doctoral dissertation, titled "On congruences between modular forms", under the supervision of Andrew Wiles. He was an assistant lecturer, lecturer, and then reader at the University of Cambridge from 1988 to 1995. From 1995 to 1996 he held the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frédéric Hélein
Frédéric Hélein (born 22 April 1963) is a French mathematician. He is university professor at Paris Diderot University. Hélein earned his doctorate at École polytechnique under supervision of Jean-Michel Coron. In 1998 Hélein was an Invited Speaker of the International Congress of Mathematicians in Berlin. He won the 1999 Fermat Prize, jointly with Fabrice Bethuel, for several important contributions to the theory of variational calculus The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t .... Notable publications Research articles * Frédéric Hélein. ''Régularité des applications faiblement harmoniques entre une surface et une variété riemannienne.'' C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 8, 591–596. * Fabrice Bethuel, Haïm Brezis, and Frédéric Hélein. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variational Calculus
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as ''geodesics''. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fabrice Béthuel
Fabrice Bethuel (born 7 June 1963) 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. In 1998 Bethuel was an Invited Speaker of the International Congress of Mathematicians in Berlin. He won the 1999 Fermat Prize, jointly with Frédéric Hélein, for several important contributions to the theory of variational calculus The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t .... He also won the 2003 for his fundamental discoveries at the interface between analysis, topology, geometry, and physics. Notable publications Research articles * Fabrice Bethuel and Xiao Min Zheng. ''Density of smooth functions between two manifolds in Sobolev spaces.'' J. Funct. Anal. 80 (198 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michel Talagrand
Michel Pierre Talagrand (; born 15 February 1952) is a French mathematician working in probability theory, functional analysis and mathematical physics. Doctor of Science since 1977, he has been, since 1985, directeur de recherches at CNRS and a member of the Functional Analysis Team of the Institut de mathématiques de Jussieu in Paris. Talagrand was also a faculty member at The Ohio State University for more than fifteen years. Talagrand was elected as correspondent of the Académie des sciences of Paris in March 1997, and then as a full member in November 2004, in the Mathematics section. In 2024, Talagrand received the Abel Prize. Talagrand studies mainly functional analysis and probability theory and their applications. Career Talagrand has been interested in probability with minimal structure. He has obtained a complete characterization of bounded Gaussian processes in very general settings, and also new methods to bound stochastic processes. He discovered new aspects o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
