|
Claude Chevalley
Claude Chevalley (; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a founding member of the Bourbaki group. Life His father, Abel Chevalley, was a French diplomat who, jointly with his wife Marguerite Chevalley née Sabatier, wrote ''The Concise Oxford French Dictionary''. Chevalley graduated from the École Normale Supérieure in 1929, where he studied under Émile Picard. He then spent time at the University of Hamburg, studying under Emil Artin and at the University of Marburg, studying under Helmut Hasse. In Germany, Chevalley discovered Japanese mathematics in the person of Shokichi Iyanaga. Chevalley was awarded a doctorate in 1933 from the University of Paris for a thesis on class field theory. When World War II broke out, Chevalley was at Princeton University. After reporting to the French Embassy, h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannesburg
Johannesburg ( , , ; Zulu and xh, eGoli ), colloquially known as Jozi, Joburg, or "The City of Gold", is the largest city in South Africa, classified as a megacity, and is one of the 100 largest urban areas in the world. According to Demographia, the Johannesburg–Pretoria urban area (combined because of strong transport links that make commuting feasible) is the 26th-largest in the world in terms of population, with 14,167,000 inhabitants. It is the provincial capital and largest city of Gauteng, which is the wealthiest province in South Africa. Johannesburg is the seat of the Constitutional Court, the highest court in South Africa. Most of the major South African companies and banks have their head offices in Johannesburg. The city is located in the mineral-rich Witwatersrand range of hills and is the centre of large-scale gold and diamond trade. The city was established in 1886 following the discovery of gold on what had been a farm. Due to the extremely large gold de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lê Dũng Tráng
Lê Dũng Tráng, (born 1947 in Saigon) is a Vietnamese-French mathematician. Life and work In the 1950s, Lê Dũng Tráng came to France, where he attended the Lycée Louis-le-Grand in Paris. He obtained a Ph.D. degree at the University of Paris in 1969 and 1971 under the supervision of Claude Chevalley and Pierre Deligne. From 1975 to 1999, he was professor at the University of Paris VII and research director of the CNRS. From 1983 to 1995 he was also a professor at the École Polytechnique. From 2002 to 2009 he headed the department of mathematics at the International Centre for Theoretical Physics (ICTP), in Trieste, Italy. He was a frequent guest scientist at Harvard University (with Phillip Griffiths) and Northeastern University (with Terence Gaffney and David B. Massey). He is particularly concerned with singularity theory in the complex domain ( Milnor fibrations, perverse sheaves). In 2000 he was involved in promoting scientific exchange between the United States ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emil Artin
Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing largely to class field theory and a new construction of L-functions. He also contributed to the pure theories of rings, groups and fields. Along with Emmy Noether, he is considered the founder of modern abstract algebra. Early life and education Parents Emil Artin was born in Vienna to parents Emma Maria, née Laura (stage name Clarus), a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of mixed Austrian and Armenian descent. His Armenian last name was Artinian which was shortened to Artin. Several documents, including Emil's birth certificate, list the father's occupation as “opera singer” though others list it as “art dealer.” It seems at least plausible that he and Emma had ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Émile Picard
Charles Émile Picard (; 24 July 1856 – 11 December 1941) was a French mathematician. He was elected the fifteenth member to occupy seat 1 of the Académie française in 1924. Life He was born in Paris on 24 July 1856 and educated there at the Lycée Henri-IV. He then studied mathematics at the École Normale Supérieure. Picard's mathematical papers, textbooks, and many popular writings exhibit an extraordinary range of interests, as well as an impressive mastery of the mathematics of his time. Picard's little theorem states that every nonconstant entire function takes every value in the complex plane, with perhaps one exception. Picard's great theorem states that an analytic function with an essential singularity takes every value infinitely often, with perhaps one exception, in any neighborhood of the singularity. He made important contributions in the theory of differential equations, including work on Picard–Vessiot theory, Painlevé transcendents and his introduction o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Auguste Sabatier
Louis Auguste Sabatier (; 22 October 1839 – 12 April 1901), French Protestant theologian, was born at Vallon-Pont-d'Arc, Ardèche and died in Strasbourg. He was educated at the Protestant theological faculty of Montauban as well as at the universities of Tübingen and Heidelberg. After holding the pastorate at Aubenas in Ardèche from 1864 to 1868, he was appointed professor of reformed dogmatics at the Protestant theological faculty of Strasbourg. His markedly French sympathies during the War of 1870 led to his expulsion from Strassburg in 1872. After five years' effort he succeeded in establishing a Protestant Faculty of Theology in Paris (today: Faculté de théologie protestante de Paris) along with Eugène Ménégoz, and became professor and then dean. In 1886, he became a teacher in the newly founded religious science department of the École des Hautes Etudes at the Sorbonne. His brother, Paul, was a noted theological historian. He is the father of two daughters ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Groups
In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups; for example, orthogonal groups, general linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally in algebraic geometry, such as elliptic curves and Jacobian varieties. An important class of algebraic groups is given by the affine algebraic groups, those whose underlying algebraic variety is an affine variety; they are exactly the algebraic subgroups of the general linear group, and are therefore also called ''linear algebraic groups''. Another class is formed by the abelian varieties, which are the algebraic groups whose underlying variety is a projective variety. Chevalley's structure theorem s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Group Theory
Finite is the opposite of infinite. It may refer to: * Finite number (other) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked for person and/or tense or aspect * "Finite", a song by Sara Groves from the album '' Invisible Empires'' See also * * Nonfinite (other) Nonfinite is the opposite of finite * a nonfinite verb is a verb that is not capable of serving as the main verb in an independent clause * a non-finite clause In linguistics, a non-finite clause is a dependent or embedded clause that represen ... {{disambiguation fr:Fini it:Finito ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class Field Theory
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credited as one of pioneers of the notion of a class field. However, this notion was already familiar to Kronecker and it was actually Weber who coined the term before Hilbert's fundamental papers came out. The relevant ideas were developed in the period of several decades, giving rise to a set of conjectures by Hilbert that were subsequently proved by Takagi and Artin (with the help of Chebotarev's theorem). One of the major results is: given a number field ''F'', and writing ''K'' for the maximal abelian unramified extension of ''F'', the Galois group of ''K'' over ''F'' is canonically isomorphic to the ideal class group of ''F''. This statement was generalized to the so called Artin reciprocity law; in the idelic language, writing ''CF' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of 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 are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chevalley Scheme
A Chevalley scheme in algebraic geometry was a precursor notion of scheme theory. Let ''X'' be a separated integral noetherian scheme In algebraic geometry, a noetherian scheme is a scheme that admits a finite covering by open affine subsets \operatorname A_i, A_i noetherian rings. More generally, a scheme is locally noetherian if it is covered by spectra of noetherian rings. Thus ..., ''R'' its function field. If we denote by X' the set of subrings \mathcal O_x of ''R'', where ''x'' runs through ''X'' (when X=\mathrm(A), we denote X' by L(A)), X' verifies the following three properties * For each M\in X' , ''R'' is the field of fractions of ''M''. * There is a finite set of noetherian subrings A_i of ''R'' so that X'=\cup_i L(A_i) and that, for each pair of indices ''i,j'', the subring A_ of ''R'' generated by A_i \cup A_j is an A_i-algebra of finite type. * If M\subseteq N in X' are such that the maximal ideal of ''M'' is contained in that of ''N'', then ''M=N''. Originally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
