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Récoltes Et Semailles
Alexander Grothendieck, later Alexandre Grothendieck in French (; ; ; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century. Grothendieck began his productive and public career as a mathematician in 1949. In 1958, he was appointed a research professor at the Institut des hautes études scientifiques (IHÉS) and remained there until 1970, when, driven by personal and political convictions, he left following a dispute over military funding. He received the Fields Medal in 1966 for advances in algebraic geometry, homological algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free State Of Prussia
The Free State of Prussia (, ) was one of the States of the Weimar Republic, constituent states of Weimar Republic, Germany from 1918 to 1947. The successor to the Kingdom of Prussia after the defeat of the German Empire in World War I, it continued to be the dominant state in Germany during the Weimar Republic, as it had been during the empire, even though most of Territorial evolution of Germany#Territorial changes after World War I, Germany's post-war territorial losses in Europe had come from its lands. It was home to the federal capital Berlin and had 62% of Germany's territory and 61% of its population. Prussia changed from the authoritarian state it had been in the past and became a parliamentary democracy under its Constitution of Prussia (1920), 1920 constitution. During the Weimar period it was governed almost entirely by pro-democratic parties and proved more politically stable than the Republic itself. With only brief interruptions, the Social Democratic Party of Germ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Messing
William Messing is an American mathematician who works in the field of arithmetic algebraic geometry. Messing received his doctorate in 1971 at Princeton University under the supervisions of Alexander Grothendieck (and Nicholas Katz) with his thesis entitled ''The Crystals Associated to Barsotti–Tate Groups: With Applications to Abelian Schemes.'' In 1972, he was a C.L.E. Moore instructor at Massachusetts Institute of Technology. He is currently professor emeritus at the University of Minnesota (Minneapolis). In his thesis, Messing elaborated on Grothendieck's 1970 lecture at the International Congress of Mathematicians in Nice on p-divisible groups ( Barsotti–Tate groups) that are important in algebraic geometry in prime characteristic, which were introduced in the 1950s by Dieudonné in his study of Lie algebras over fields of finite characteristic. Messing worked together with Pierre Berthelot, Barry Mazur Barry Charles Mazur (; born December 19, 1937) is an America ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Torsion (mechanics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a Set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of List of continuity-related mathematical topics, continuity. Euclidean spaces, and, more generally, metric spaces are examples of topological spaces, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and Homotopy, homotopies. A property that is invariant under such deformations is a to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory can often be understood through the study of Complex analysis, analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic variety, algebraic varieties, which are geometric manifestations of solution set, solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are line (geometry), lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscate of Bernoulli, lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular point of a curve, singular p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crafoord Prize
The Crafoord Prize () is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord following a donation to the Royal Swedish Academy of Sciences. It is awarded jointly by the Academy and the Crafoord Foundation in Lund, with the former selecting the laureates. The Prize is awarded in four categories: mathematics and astronomy, Geology, geosciences, Biology, biosciences (with an emphasis on ecology) and polyarthritis, the final one because Holger suffered from severe rheumatoid arthritis in his later years. The disciplines for which the Crafoord Prize is awarded are chosen so as to complement the Nobel Prizes. Only one award is given each year, according to a rotating scheme – astronomy and mathematics, then geosciences, then biosciences. Since 2012, the prizes in astronomy and mathematics are separate and awarded at the same time; prior to this, the disciplines alternated every cycle. A Crafoord Prize in polyarth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Émile Picard Medal
The Émile Picard Medal (or Médaille Émile Picard) is a medal named for Émile Picard awarded every 6 years to an outstanding mathematician by the Institut de France, Académie des sciences. This rewards a mathematician designated by the Academy of Sciences every six years. The first medal was awarded in 1946. Recipients The Émile Picard Medal recipients are * Maurice Fréchet (1946) * Paul Lévy (1953) * Henri Cartan (1959) * Szolem Mandelbrojt (1965), * Jean-Pierre Serre (1971) * Alexandre Grothendieck (1977) * André Néron (1983) * François Bruhat (1989) * Jean-Pierre Kahane (1995) * Jacques Dixmier (2001) * Louis Boutet de Monvel (2007) * Luc Illusie (2012) * Yves Colin de Verdière (2018) See also * List of mathematics awards This list of mathematics awards contains articles about notable awards for mathematics. The list is organized by the region and country of the organization that sponsors the award, but awards may be open to mathematicians from around the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been list of prizes known as the Nobel or the highest honors of a field, described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by Academic Ranking of World Universities, ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG Observatory on Academic Ranking and Excellence, IR ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homological Algebra
Homological algebra is the branch of mathematics that studies homology (mathematics), homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of module (mathematics), modules and Syzygy (mathematics), syzygies) at the end of the 19th century, chiefly by Henri Poincaré and David Hilbert. Homological algebra is the study of homological functors and the intricate algebraic structures that they entail; its development was closely intertwined with the emergence of category theory. A central concept is that of chain complexes, which can be studied through their homology and cohomology. Homological algebra affords the means to extract information contained in these complexes and present it in the form of homological invariant (mathematics), invariants of ring (mathematics), rings, modules, topological spaces, and other "tangible ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic variety, algebraic varieties, which are geometric manifestations of solution set, solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are line (geometry), lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscate of Bernoulli, lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular point of a curve, singular p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, or Topological space#Definitions, topology) and the linear transformation, linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous function, continuous or unitary operator, unitary operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Louis Verdier
Jean-Louis Verdier (; 2 February 1935 – 25 August 1989) was a French mathematician who worked, under the guidance of his doctoral advisor Alexander Grothendieck, on derived categories and Verdier duality. He was a close collaborator of Grothendieck, notably contributing to SGA 4 his theory of hypercovers and anticipating the later development of étale homotopy by Michael Artin and Barry Mazur, following a suggestion he attributed to Pierre Cartier. Saul Lubkin's related theory of rigid hypercovers was later taken up by Eric Friedlander in his definition of the étale topological type. Verdier was a student at the elite École Normale Supérieure in Paris, and later became director of studies there, as well as a Professor at the University of Paris VII. For many years he directed a joint seminar at the École Normale Supérieure with Adrien Douady. Verdier was a member of Bourbaki. In 1984 he was the president of the Société Mathématique de France. In 1976 Ver ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
