|
Alain Lascoux
Alain Lascoux (17 October 1944 – 20 October 2013) was a French mathematician at Université de Paris VII, University of Marne la Vallée and Nankai University. His research was primarily in algebraic combinatorics, particularly Affine Hecke algebra, Hecke algebras and Young tableaux. Lascoux earned his doctorate in 1977 from the University of Paris. He worked for twenty years with Marcel-Paul Schützenberger on properties of the symmetric group. They wrote many articles together and had a major impact on the development of algebraic combinatorics. They succeeded in giving a combinatorial understanding of various algebraic and geometric questions in representation theory. Thus they introduced many new objects related to both fields like Schubert polynomials and Grothendieck polynomials, as well as novel terminology like the plactic monoid and vexillary permutation, vexillary permutations. They were also the first to define the Crystal bases, crystal graph structure on Young table ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
France
France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlantic, North Atlantic, the French West Indies, and List of islands of France, many islands in Oceania and the Indian Ocean, giving it Exclusive economic zone of France, one of the largest discontiguous exclusive economic zones in the world. Metropolitan France shares borders with Belgium and Luxembourg to the north; Germany to the northeast; Switzerland to the east; Italy and Monaco to the southeast; Andorra and Spain to the south; and a maritime border with the United Kingdom to the northwest. Its metropolitan area extends from the Rhine to the Atlantic Ocean and from the Mediterranean Sea to the English Channel and the North Sea. Its Regions of France, eighteen integral regions—five of which are overseas—span a combined area of and hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grothendieck Polynomials
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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2013 Deaths
This is a list of lists of deaths of notable people, organized by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked below. 2025 2024 2023 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 1986 Earlier years ''Deaths in years earlier than this can usually be found in the main articles of the years.'' See also * Lists of deaths by day * Deaths by year (category) {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris Alumni
A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Universities typically offer both undergraduate and postgraduate programs. The first universities in Europe were established by Catholic monks. The University of Bologna (), Italy, which was founded in 1088, is the first university in the sense of: *being a high degree-awarding institute. *using the word (which was coined at its foundation). *having independence from the ecclesiastic schools and issuing secular as well as non-secular degrees (with teaching conducted by both clergy and non-clergy): grammar, rhetoric, logic, theology, canon law and notarial law.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2008, , p. 55f.de Ridder-Symoens, Hilde''A History of the University in Europe: Volume 1, Universities i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1944 Births
Events Below, the events of World War II have the "WWII" prefix. January * January 2 – WWII: ** Free France, Free French General Jean de Lattre de Tassigny is appointed to command First Army (France), French Army B, part of the Sixth United States Army Group in North Africa. ** Landing at Saidor: 13,000 US and Australian troops land on Papua New Guinea in an attempt to cut off a Japanese retreat. * January 8 – WWII: Philippine Commonwealth troops enter the province of Ilocos Sur in northern Luzon and attack Japanese forces. * January 11 ** United States President Franklin D. Roosevelt proposes a Second Bill of Rights for social and economic security, in his State of the Union address. ** The Nazi German administration expands Kraków-Płaszów concentration camp into the larger standalone ''Konzentrationslager Plaszow bei Krakau'' in occupied Poland. * January 12 – WWII: Winston Churchill and Charles de Gaulle begin a 2-day conference in Marrakech. * Janua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LLT Polynomial
In mathematics, an LLT polynomial is one of a family of symmetric functions introduced as ''q''-analogues of products of Schur functions. J. Haglund, M. Haiman, and N. Loehr showed how to expand Macdonald polynomials in terms of LLT polynomials. Ian Grojnowski and Mark Haiman proved a positivity conjecture for LLT polynomials that combined with the previous result implies the Macdonald positivity conjecture for Macdonald polynomials, and extended the definition of LLT polynomials to arbitrary finite root systems.I. Grojnowski, M. Haiman, ''Affine algebras and positivity'' (preprint availablhere References *I. Grojnowski, M. Haiman, ''Affine algebras and positivity'' (preprint availablhere *J. Haglund, M. Haiman, N. LoehA Combinatorial Formula for Macdonald Polynomials J. Amer. Math. Soc. 18 (2005), no. 3, 735–761 *Alain Lascoux, Bernard Leclerc, and Jean-Yves ThiboRibbon Tableaux, Hall-Littlewood Functions, Quantum Affine Algebras and Unipotent Varieties J. Math. Ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Germany
Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total population of over 84 million in an area of , making it the most populous member state of the European Union. It borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, and France, Luxembourg, Belgium, and the Netherlands to the west. The Capital of Germany, nation's capital and List of cities in Germany by population, most populous city is Berlin and its main financial centre is Frankfurt; the largest urban area is the Ruhr. Settlement in the territory of modern Germany began in the Lower Paleolithic, with various tribes inhabiting it from the Neolithic onward, chiefly the Celts. Various Germanic peoples, Germanic tribes have inhabited the northern parts of modern Germany since classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population within city limits, highest population within its city limits of any city in the European Union. The city is also one of the states of Germany, being the List of German states by area, third smallest state in the country by area. Berlin is surrounded by the state of Brandenburg, and Brandenburg's capital Potsdam is nearby. The urban area of Berlin has a population of over 4.6 million and is therefore the most populous urban area in Germany. The Berlin/Brandenburg Metropolitan Region, Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's second-largest metropolitan region after the Rhine-Ruhr region, as well as the List of EU metropolitan areas by GDP, fifth-biggest metropolitan region by GDP in the European Union. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before 2022 as the Nevanlinna Prize), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History German mathematicians Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review. ''CMS Notes'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal Bases
A crystal base for a representation of a quantum group on a \Q(v)-vector space In mathematics and physics, a vector space (also called a linear space) is a set (mathematics), set whose elements, often called vector (mathematics and physics), ''vectors'', can be added together and multiplied ("scaled") by numbers called sc ... is not a base of that vector space but rather a \Q-base of L/vL where L is a \Q(v)-lattice in that vector space. Crystal bases appeared in the work of and also in the work of . They can be viewed as specializations as v \to 0 of the canonical basis defined by . Definition As a consequence of its defining relations, the quantum group U_q(G) can be regarded as a Hopf algebra over the field of all rational functions of an indeterminate ''q'' over \Q, denoted \Q(q). For simple root \alpha_i and non-negative integer n, define :\begin e_i^ = f_i^ &= 1 \\ e_i^ &= \frac \\ ptf_i^ &= \frac \end In an integrable module M, and for weight \lambda, a vect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vexillary Permutation
In mathematics, a vexillary permutation is a permutation ''μ'' of the positive integers containing no subpermutation isomorphic to the permutation (2143); in other words, there do not exist four numbers ''i'' < ''j'' < ''k'' < ''l'' with ''μ''(''j'') < ''μ''(''i'') < ''μ''(''l'') < ''μ''(''k''). They were introduced by . The word "vexillary" means flag-like, and comes from the fact that vexillary permutations are related to flags
A flag is a piece of fabric (most often rectangular) with distinctive colours and design. It is used as a symbol, a signalling device, or for decoration. The term ''flag'' is also used to refer to the graphic design employed, and flags have ... of [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
