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Pierre 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 1965, 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 theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Etterbeek
Etterbeek (; ) is one of the List of municipalities of the Brussels-Capital Region, 19 municipalities of the Brussels-Capital Region, Belgium. Located in the eastern part of the region, it is bordered by the municipalities of Auderghem, the City of Brussels, Ixelles, Schaerbeek, Woluwe-Saint-Lambert and Woluwe-Saint-Pierre. In common with all of Brussels' municipalities, it is legally Multilingualism, bilingual (French–Dutch). History Origins and etymology According to legend, Saint Gertrude of Nivelles, daughter of Pippin of Landen, founded a chapel there in the 8th century. A document by Otto I, Holy Roman Emperor, dated 966, mentions the church of ''Iatrebache''. The name ''Ietrebecca''—possibly from the Celtic languages, Celtic root ''ett'' meaning "rapid movement" and the Dutch word ''beek'' meaning "stream"—is found for the first time in a document dated 1127. The current spelling appears eleven years later in 1138, around which time a newer and larger church was bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balzan Prize
The International Balzan Prize Foundation awards four annual monetary prizes to people or organizations who have made outstanding achievements in the fields of humanities, natural sciences, culture, as well as for endeavours for peace and the brotherhood of man. History The assets behind the foundation were established by the Italian Eugenio Balzan (1874–1953), a part-owner of who had invested his assets in Switzerland and in 1933 had left Italy in protest against fascism. He left a substantial inheritance to his daughter Angela Lina Balzan (1892–1956), who at the time was suffering an incurable disease. Before her death, she left instructions for the foundation and since then it has two headquarters, the Prize administered from Milan, the Fund from Zurich. The first award was in fact one million Swiss francs to the Nobel Foundation in 1961. After 1962, a gap of 16 years followed when prizes recommenced with an award of half a million Swiss francs to Mother Teresa. Award ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hodge Theory
In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold ''M'' using partial differential equations. The key observation is that, given a Riemannian metric on ''M'', every cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric. Such forms are called harmonic. The theory was developed by Hodge in the 1930s to study algebraic geometry, and it built on the work of Georges de Rham on de Rham cohomology. It has major applications in two settings—Riemannian manifolds and Kähler manifolds. Hodge's primary motivation, the study of complex projective varieties, is encompassed by the latter case. Hodge theory has become an important tool in algebraic geometry, particularly through its connection to the study of algebraic cycles. While Hodge theory is intrinsically dependent upon the real and complex numbers, it can be applied to questions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
L-function
In mathematics, an ''L''-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An ''L''-series is a Dirichlet series, usually convergent on a half-plane, that may give rise to an ''L''-function via analytic continuation. The Riemann zeta function is an example of an ''L''-function, and some important conjectures involving ''L''-functions are the Riemann hypothesis and its generalizations. The 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 still out of reach of proof, are set out in a systematic way. Because of the Euler product formula there is a deep connection between ''L''-functions and the theory of prime numbers. The mathematical field tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Equation
In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations. However, a more restricted meaning is often used, where a ''functional equation'' is an equation that relates several values of the same function. For example, the logarithm functions are essentially characterized by the ''logarithmic functional equation'' \log(xy)=\log(x) + \log(y). If the domain of the unknown function is supposed to be the natural numbers, the function is generally viewed as a sequence, and, in this case, a functional equation (in the narrower meaning) is called a recurrence relation. Thus the term ''functional equation'' is used mainly for real functions and complex functions. Moreover a smoothness condition is often assumed for the solutions, since without such a condition, most functional equations have very irregular solutions. For example, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Form
In mathematics, a modular form is a holomorphic function on the complex upper half-plane, \mathcal, that roughly satisfies a functional equation with respect to the group action of the modular group and a growth condition. The theory of modular forms has origins in complex analysis, with important connections with number theory. Modular forms also appear in other areas, such as algebraic topology, sphere packing, and string theory. Modular form theory is a special case of the more general theory of automorphic forms, which are functions defined on Lie groups that transform nicely with respect to the action of certain discrete subgroups, generalizing the example of the modular group \mathrm_2(\mathbb Z) \subset \mathrm_2(\mathbb R). Every modular form is attached to a Galois representation. The term "modular form", as a systematic description, is usually attributed to Erich Hecke. The importance of modular forms across multiple field of mathematics has been humorously re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Pierre Serre
Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003. Biography Personal life Born in Bages, Pyrénées-Orientales, to pharmacist parents, Serre was educated at the Lycée de Nîmes. Then he studied at the École Normale Supérieure in Paris from 1945 to 1948. He was awarded his doctorate from the Sorbonne in 1951. From 1948 to 1954 he held positions at the Centre National de la Recherche Scientifique in Paris. In 1956 he was elected professor at the Collège de France, a position he held until his retirement in 1994. His wife, Professor Josiane Heulot-Serre, was a chemist; she also was the director of the Ecole Normale Supérieure de Jeunes Filles. Their daughter is the former French diplomat, historian and writer Claudine Monteil. The French mathematician D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zariski's Main Theorem
In algebraic geometry, Zariski's main theorem, proved by , is a statement about the structure of birational morphisms stating roughly that there is only one branch at any normal point of a variety. It is the special case of Zariski's connectedness theorem when the two varieties are birational. Zariski's main theorem can be stated in several ways which at first sight seem to be quite different, but are in fact deeply related. Some of the variations that have been called Zariski's main theorem are as follows: *A birational morphism with finite fibers to a normal variety is an isomorphism to an open subset. *The total transform of a normal fundamental point of a birational map has positive dimension. This is essentially Zariski's original version. *The total transform of a normal point under a proper birational morphism is connected. *A generalization due to Grothendieck describes the structure of quasi-finite morphisms of schemes. Several results in commutative algebra imply the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scheme Theory
In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations and define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers). Scheme theory was introduced by Alexander Grothendieck in 1960 in his treatise '' Éléments de géométrie algébrique'' (EGA); one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne). Strongly based on commutative algebra, scheme theory allows a systematic use of methods of topology and homological algebra. Scheme theory also unifies algebraic geometry with much of number theory, which eventually led to Wiles's proof of Fermat's Last Theorem. Schemes elaborate the fundamental idea that an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orsay
Orsay () is a Communes of France, commune in the Essonne Departments of France, department in Île-de-France in northern France. It is located in the southwestern suburbs of Paris, France, from the Kilometre Zero, centre of Paris. A fortified location of the Vallée de Chevreuse, Chevreuse valley since the 8th century and agricultural domain of wealthy and influential people, the development of Orsay is marked by the introduction of a Rail transport, railroad in the second half of the 18th century (today the RER B of which two stations are located in Orsay) and donations which allow the construction of a hospital still active to this day. Orsay is the main home to the Paris-Saclay University. The university significantly shapes Orsay's economy as it employs about 10,000 academic workers. The city's economy is also centered on high technology, with several companies drawn to the area by the Paris-Saclay's research and development infrastructure. Seat of the Orsay campus of Pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris-Sud
Paris-Sud University (), also known as the University of Paris — XI (or as the Orsay Faculty of Sciences, University of Paris before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, including Orsay, Cachan, Châtenay-Malabry, Sceaux, Hauts-de-Seine, Sceaux, and Kremlin-Bicêtre campuses. In 2019, the university was replaced by the Paris-Saclay University. History Paris-Sud, as the Orsay Faculty of Sciences, was originally part of the University of Paris, which was subsequently split into several universities. After World War II, the rapid growth of nuclear physics and chemistry meant that research needed more and more powerful accelerators, which required large areas. The University of Paris, the and the looked for space in the south of Paris near Orsay. Later some of the teaching activity of the Faculty of Sciences in Paris was transferred to Orsay in 1956 at the request of Irène Joliot-Curie and Frédéric Joli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Athénée Adolphe Max
The Athénée Adolphe Max (AAM) is a French-language secondary school in Brussels, Belgium, which is part of the official education network. It is located to the east of the City of Brussels, near the Squares Quarter. History 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 the Athénée Adolphe Max after the mayor of Brussels Adolphe Max. In 1978, the two secondary schools merged into a single athenaeum and adopted the name Athénée Adolphe Max in 1990. Description The Athénée Adolphe Max is a school based on the promotion of effort in a respectful setting. The objective of the athenaeum 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 cour ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
