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Deligne
Pierre René, Viscount Deligne (; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal. Early life and education Deligne was born in Etterbeek, attended school at Athénée Adolphe Max and studied at the Université libre de Bruxelles (ULB), writing a dissertation titled ''Théorème de Lefschetz et critères de dégénérescence de suites spectrales'' (Theorem of Lefschetz and criteria of degeneration of spectral sequences). He completed his doctorate at the University of Paris-Sud in Orsay 1972 under the supervision of Alexander Grothendieck, with a thesis titled ''Théorie de Hodge''. Career Starting in 1972, Deligne worked with Grothendieck at the Institut des Hautes Études Scientifiques (IHÉS) near Paris, initially on the generalization within scheme theory of Zariski's main theorem. In 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weil Conjectures
In mathematics, the Weil conjectures were highly influential proposals by . They led to a successful multi-decade program to prove them, in which many leading researchers developed the framework of modern algebraic geometry and number theory. The conjectures concern the generating functions (known as local zeta functions) derived from counting points on algebraic varieties over finite fields. A variety over a finite field with elements has a finite number of rational points (with coordinates in the original field), as well as points with coordinates in any finite extension of the original field. The generating function has coefficients derived from the numbers of points over the extension field with elements. Weil conjectured that such ''zeta functions'' for smooth varieties are rational functions, satisfy a certain functional equation, and have their zeros in restricted places. The last two parts were consciously modelled on the Riemann zeta function, a kind of generating f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perverse Sheaves
The mathematical term perverse sheaves refers to a certain abelian category associated to a topological space ''X'', which may be a real or complex manifold, or a more general topologically stratified space, usually singular. This concept was introduced in the thesis of Zoghman Mebkhout, gaining more popularity after the (independent) work of Joseph Bernstein, Alexander Beilinson, and Pierre Deligne (1982) as a formalisation of the Riemann-Hilbert correspondence, which related the topology of singular spaces (intersection homology of Mark Goresky and Robert MacPherson) and the algebraic theory of differential equations ( microlocal calculus and holonomic D-modules of Joseph Bernstein, Masaki Kashiwara and Takahiro Kawai). It was clear from the outset that perverse sheaves are fundamental mathematical objects at the crossroads of algebraic geometry, topology, analysis and differential equations. They also play an important role in number theory, algebra, and representation th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Stack
In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli spaces are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of pointed algebraic curves \mathcal_ and the moduli stack of elliptic curves. Originally, they were introduced by Grothendieck to keep track of automorphisms on moduli spaces, a technique which allows for treating these moduli spaces as if their underlying schemes or algebraic spaces are smooth. But, through many generalizations the notion of algebraic stacks was finally discovered by Michael Artin. Definition Motivation One of the motivating examples of an algebraic stack is to consider a groupoid scheme (R,U,s,t,m) over a fixed scheme S. For example, if R = \mu_n\times_S\mathbb^n_S (where \mu_n is the group scheme of roots of unity), U = \mathbb^n_S, s = \text_U is ... [...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. The Prize is awarded in partnership between the Royal Swedish Academy of Sciences and the Crafoord Foundation in Lund. The Academy is responsible for selecting the Crafoord Laureates. The prize is awarded in four categories: astronomy and mathematics; Geology, geosciences; Biology, biosciences, with particular emphasis on ecology; and polyarthritis, the disease from which Holger severely suffered in his last years. According to the Academy, "these disciplines are chosen so as to complement those for which the Nobel Prizes are awarded". Only one award is given each year, according to a rotating scheme – astronomy and mathematics; then geosciences; then biosciences. A Crafoord Prize in polyarthritis is only awarded when a special committee decides that substantial progress in the field has been made. The recipient of the Crafoord Prize is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moduli Space
In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects. A variant of moduli spaces is formal moduli. Motivation Moduli spaces are spaces of solutions of geometric classification problems. That is, the points of a moduli space correspond to solutions of geometric problems. Here different solutions are identified if they a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Rapoport
Michael Rapoport (born 2 October 1948) is an Austrian mathematician. Career Rapoport received his PhD from Paris-Sud 11 University in 1976, under the supervision of Pierre Deligne. He held a chair for arithmetic algebraic geometry at the University of Bonn, as well as a visiting appointment at the University of Maryland. In 1992, he was awarded the Gottfried Wilhelm Leibniz Prize, DFG in 1999 he won the Gay-Lussac Humboldt Prize, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abel Prize
The Abel Prize ( ; no, Abelprisen ) is awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Prizes. It comes with a monetary award of 7.5 million Norwegian kroner (NOK; increased from 6 million NOK in 2019). The Abel Prize's history dates back to 1899, when its establishment was proposed by the Norwegian mathematician Sophus Lie when he learned that Alfred Nobel's plans for annual prizes would not include a prize in mathematics. In 1902, King Oscar II of Sweden and Norway indicated his willingness to finance the creation of a mathematics prize to complement the Nobel Prizes, but the establishment of the prize was prevented by the dissolution of the union between Norway and Sweden in 1905. It took almost a century before the prize was finally established by the Government of Norway in 2001, and it was specifically intended "to give t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the Group action (mathematics), group action of the modular group, and also satisfying a growth condition. The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections with number theory. Modular forms appear in other areas, such as algebraic topology, sphere packing, and string theory. A modular function is a function that is invariant with respect to the modular group, but without the condition that be Holomorphic function, holomorphic in the upper half-plane (among other requirements). Instead, modular functions are Meromorphic function, meromorphic (that is, they are holomorphic on the complement of a set of isolated points, which are poles of the function). Modular form theory is a special case of the more general theory of automorphic form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory has contributed a number of advances to mathematical physics, which have been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, and conde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Athénée Adolphe Max
Athénée Adolphe Max is a secondary school of the City of Brussels which is part of the official education network;. It is located to the east of the center of Brussels, near the Squares district . Historical A first building was designed in 1904 by the architect Edmond De Vigne . In 1909 two secular schools were created. A first Carter high school for girls, later named Carter in homage to the first director, and an athenaeum for boys, later named Athénée Adolphe Max after the famous mayor of Brussels Adolphe Max. In 1978, the two secondary schools merged into a single athénée and adopted the name Athénée Adolphe Max in 1990. Description The Adolphe Max Athenaeum is a school based on the promotion of effort in a respectful setting. The objective of the athénée is to transmit quality training to develop their intellectual and moral skills so that they have the level to approach higher education successfully. The school has two courtyards : * the Carter courtyard mad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris-Sud
Paris-Sud University (French: ''Université Paris-Sud''), also known as University of Paris — XI (or as Université d'Orsay before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, including Orsay, Cachan, Châtenay-Malabry, Sceaux, and Kremlin-Bicêtre campuses. The main campus was located in Orsay. Starting from 2020, University Paris Sud has been replaced by the University of Paris-Saclay in The League of European Research Universities (LERU). Paris-Sud was one of the largest and most prestigious universities in France, particularly in science and mathematics. The university was ranked 1st in France, 9th in Europe and 37th worldwide by 2019 Academic Ranking of World Universities (ARWU) in particular it was ranked as 1st in Europe for physics and 2nd in Europe for mathematics. Five Fields Medalists and two Nobel Prize Winners have been affiliated to the university. On 16 January 2019, Alain Sarfati was electe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miles Reid
Miles Anthony Reid FRS (born 30 January 1948) is a mathematician who works in algebraic geometry. Education Reid studied the Cambridge Mathematical Tripos at Trinity College, Cambridge and obtained his Ph.D. in 1973 under the supervision of Peter Swinnerton-Dyer and Pierre Deligne. Career Reid was a research fellow of Christ's College, Cambridge from 1973 to 1978. He became a lecturer at the University of Warwick in 1978 and was appointed professor there in 1992. He has written two well known books: ''Undergraduate Algebraic Geometry'' and ''Undergraduate Commutative Algebra''. Awards and honours Reid was elected a Fellow of the Royal Society in 2002. In the same year, he participated as an Invited Speaker in the International Congress of Mathematicians in Beijing. Reid was awarded the Senior Berwick Prize in 2006 for his paper with Alessio Corti and Aleksandr Pukhlikov, "Fano 3-fold hypersurfaces", which made a big advance in the study of 3-dimensional algebraic variet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
