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Jean-Louis Koszul
Jean-Louis Koszul (; January 3, 1921 – January 12, 2018) was a French mathematician, best known for studying geometry and discovering the Koszul complex. He was a second generation member of Bourbaki. Biography Koszul was educated at the in Strasbourg before studying at the Faculty of Science University of Strasbourg and the Faculty of Science of the University of Paris. His Ph.D. thesis, titled ''Homologie et cohomologie des algèbres de Lie'', was written in 1950 under the direction of Henri Cartan. He lectured at many universities and was appointed in 1963 professor in the Faculty of Science at the University of Grenoble. He was a member of the French Academy of Sciences. Koszul was the cousin of the French composer Henri Dutilleux, and the grandchild of the composer Julien Koszul. Koszul married Denise Reyss-Brion on July 17, 1948. They had three children: Michel, Bertrand, and Anne. He died on January 12, 2018 at the age of 97, nine days after his 97th birthday. S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strasbourg
Strasbourg (, , ; german: Straßburg ; gsw, label=Bas Rhin Bas-Rhin (; Alsatian: ''Unterelsà ss'', ' or '; traditional german: links=no, Niederrhein; en, Lower Rhine) is a department in Alsace which is a part of the Grand Est super-region of France. The name means 'Lower Rhine', referring to its lowe ... Alsatian dialect, Alsatian, Strossburi , gsw, label=Haut Rhin Alsatian dialect, Alsatian, Strossburig ) is the Prefectures in France, prefecture and largest city of the Grand Est Regions of France, region of Geography of France, eastern France and the Seat of the European Parliament in Strasbourg, official seat of the European Parliament. Located at the France–Germany border, border with Germany in the historic region of Alsace, it is the prefecture of the Bas-Rhin Departments of France, department. In 2019, the city proper had 287,228 inhabitants and both the Eurométropole de Strasbourg (Greater Strasbourg) and the Arrondissement of Strasbourg had 505,272 inhabita ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henri Dutilleux
Henri Paul Julien Dutilleux (; 22 January 1916 – 22 May 2013) was a French composer active mainly in the second half of the 20th century. His small body of published work, which garnered international acclaim, followed in the tradition of Maurice Ravel, Claude Debussy, Albert Roussel and Olivier Messiaen, but in an idiosyncratic, individual style. Some of his notable compositions include a piano sonata, two symphonies, the cello concerto '' Tout un monde lointain…'' (''A whole distant world''), the violin concerto '' L'arbre des songes'' (''The tree of dreams''), the string quartet '' Ainsi la nuit'' (''Thus the night'') and a sonatine for flute and piano. Some of these are regarded as masterpieces of 20th-century classical music. Works were commissioned from him by such major artists as Charles Munch, George Szell, Mstislav Rostropovich, the Juilliard String Quartet, Isaac Stern, Paul Sacher, Anne-Sophie Mutter, Simon Rattle, Renée Fleming, and Seiji Ozawa. Fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Members Of The French Academy Of Sciences
Member may refer to: * Military jury, referred to as "Members" in military jargon * Element (mathematics), an object that belongs to a mathematical set * In object-oriented programming, a member of a class ** Field (computer science), entries in a database ** Member variable, a variable that is associated with a specific object * Limb (anatomy), an appendage of the human or animal body ** Euphemism for penis * Structural component of a truss, connected by nodes * User (computing), a person making use of a computing service, especially on the Internet * Member (geology), a component of a geological formation * Member of parliament A member of parliament (MP) is the representative in parliament of the people who live in their electoral district. In many countries with Bicameralism, bicameral parliaments, this term refers only to members of the lower house since upper house ... * The Members, a British punk rock band * Meronymy, a semantic relationship in linguistics * Church mem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French People Of Polish Descent
French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with France ** French cuisine, cooking traditions and practices Fortnite French places Arts and media * The French (band), a British rock band * "French" (episode), a live-action episode of ''The Super Mario Bros. Super Show!'' * ''Française'' (film), 2008 * French Stewart (born 1964), American actor Other uses * French (surname), a surname (including a list of people with the name) * French (tunic), a particular type of military jacket or tunic used in the Russian Empire and Soviet Union * French's, an American brand of mustard condiment * French catheter scale, a unit of measurement of diameter * French Defence, a chess opening * French kiss, a type of kiss involving the tongue See also * France (other) * Franch, a surname * Frenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
École Normale Supérieure Alumni
École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine The Seine ( , ) is a river in northern France. Its drainage basin is in the Paris Basin (a geological relative lowland) covering most of northern France. It rises at Source-Seine, northwest of Dijon in northeastern France in the Langres plate ... flowing in région Île-de-France * École, Savoie, a French commune * École-Valentin, a French commune in the Doubs département * Grandes écoles, higher education establishments in France * The École, a French-American bilingual school in New York City Ecole may refer to: * Ecole Software, a Japanese video-games developer/publisher {{disambiguation, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2018 Deaths
This is a list of deaths of notable people, organised by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked here. 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 See also * Lists of deaths by day * Deaths by year {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1921 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album '' 63/19'' by Kool A.D. * '' Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album ''Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Algebra Cohomology
In mathematics, Lie algebra cohomology is a cohomology theory for Lie algebras. It was first introduced in 1929 by Élie Cartan to study the topology of Lie groups and homogeneous spaces by relating cohomological methods of Georges de Rham to properties of the Lie algebra. It was later extended by to coefficients in an arbitrary Lie module. Motivation If G is a compact simply connected Lie group, then it is determined by its Lie algebra, so it should be possible to calculate its cohomology from the Lie algebra. This can be done as follows. Its cohomology is the de Rham cohomology of the complex of differential forms on G. Using an averaging process, this complex can be replaced by the complex of left-invariant differential forms. The left-invariant forms, meanwhile, are determined by their values at the identity, so that the space of left-invariant differential forms can be identified with the exterior algebra of the Lie algebra, with a suitable differential. The construction of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Koszul Cohomology
In mathematics, the Koszul cohomology groups K_(X,L) are groups associated to a projective variety ''X'' with a line bundle ''L''. They were introduced by , and named after Jean-Louis Koszul as they are closely related to the Koszul complex. surveys early work on Koszul cohomology, gives an introduction to Koszul cohomology, and gives a more advanced survey. Definitions If ''M'' is a graded module over the symmetric algebra of a vector space ''V'', then the Koszul cohomology K_(M,V) of ''M'' is the cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ... of the sequence :\bigwedge^M_\rightarrow \bigwedge^M_ \rightarrow \bigwedge^M_ If ''L'' is a line bundle over a projective variety ''X'', then the Koszul cohomology K_(X,L) is given by the Koszul cohomology K_(M,V) of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Koszul Algebra
In abstract algebra, a Koszul algebra R is a graded k-algebra over which the ground field k has a linear minimal graded free resolution, ''i.e.'', there exists an exact sequence: :\cdots \rightarrow R(-i)^ \rightarrow \cdots \rightarrow R(-2)^ \rightarrow R(-1)^ \rightarrow R \rightarrow k \rightarrow 0. Here, R(-j) is the graded algebra R with grading shifted up by j, ''i.e.'' R(-j)_i = R_. The exponents b_i refer to the b_i-fold direct sum. Choosing bases for the free modules in the resolution, the chain maps are given by matrices, and the definition requires the matrix entries to be zero or linear forms. An example of a Koszul algebra is a polynomial ring over a field, for which the Koszul complex is the minimal graded free resolution of the ground field. There are Koszul algebras whose ground fields have infinite minimal graded free resolutions, ''e.g'', R = k ,y(xy) . The concept is named after the French mathematician Jean-Louis Koszul. See also *Koszul duality In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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