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Andrey Zelevinsky
Andrei Vladlenovich Zelevinsky (; 30 January 1953 – 10 April 2013) was a Russian-American mathematician who made important contributions to algebra, combinatorics, and representation theory, among other areas. Biography Zelevinsky graduated in 1969 from the Moscow Mathematical School No. 2. After winning a silver medal as a member of the USSR team at the International Mathematical Olympiad he was admitted without examination to the mathematics department of Moscow State University where he obtained his PhD in 1978 under the mentorship of Joseph Bernstein, Alexandre Kirillov and Israel Gelfand. He worked in the mathematical laboratory of Vladimir Keilis-Borok at the Institute of Earth Science (1977–85), and at the Council for Cybernetics of the Soviet Academy of Sciences (1985–90). In the early 1980s, at a great personal risk, he taught at the Jewish People's University, an unofficial organization offering first-class mathematics education to talented students denied admiss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. When th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arkady Berenstein
Arkady (russian: Арка́дий, Arkadiy) is a Slavic masculine given name, ultimately derived from the Greek name Αρκάδιος, meaning “from Arcadia”. The Latin equivalent is Arcadius. Notable people with the name include: People: *Arkady Andreasyan (born 1947), Armenian former football player and manager * Arkadios Dimitrakopoulos (1824-1908), Greek merchant *Arcady Aris (1901–1942), Chuvash writer *Arkady Averchenko (1881–1925), Russian playwright and satirist *Arkady Babchenko (born 1977), Russian journalist *Arcady Boytler (1895–1965), Russian Mexican filmmaker *Arkady Mikhailovich Chernetsky (born 1950), mayor of Yekaterinburg, Sverdlovsk Oblast, Russia as of 2007 *Arkady Chernyshev (1914–1992), Soviet ice hockey and soccer player *Arkady Fiedler (1894–1985), Polish writer, journalist and adventurer *Arkady Filippenko (1912–1983), Soviet Ukrainian composer *Arkady Gaidar (1904–1941), Soviet writer whose stories were very popular among Soviet children ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Picture (mathematics)
In combinatorics, combinatorial mathematics, a picture is a bijection between Young tableau#Skew tableaux, skew diagrams satisfying certain properties, introduced by in a generalization of the Robinson–Schensted correspondence and the Littlewood–Richardson rule. References * *{{Citation , authorlink=Andrei Zelevinsky , last1=Zelevinsky , first1=A. V. , title=A generalization of the Littlewood-Richardson rule and the Robinson-Schensted-Knuth correspondence , doi=10.1016/0021-8693(81)90128-9 , mr=613858 , year=1981 , journal=Journal of Algebra , issn=0021-8693 , volume=69 , issue=1 , pages=82–94, doi-access=free Algebraic combinatorics Combinatorial algorithms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robinson–Schensted Correspondence
In mathematics, the Robinson–Schensted correspondence is a bijective correspondence between permutations and pairs of standard Young tableaux of the same shape. It has various descriptions, all of which are of algorithmic nature, it has many remarkable properties, and it has applications in combinatorics and other areas such as representation theory. The correspondence has been generalized in numerous ways, notably by Knuth to what is known as the Robinson–Schensted–Knuth correspondence, and a further generalization to pictures by Zelevinsky. The simplest description of the correspondence is using the Schensted algorithm , a procedure that constructs one tableau by successively inserting the values of the permutation according to a specific rule, while the other tableau records the evolution of the shape during construction. The correspondence had been described, in a rather different form, much earlier by Robinson , in an attempt to prove the Littlewood–Richardson rule. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Littlewood–Richardson Rule
In mathematics, the Littlewood–Richardson rule is a combinatorial description of the coefficients that arise when decomposing a product of two Schur functions as a linear combination of other Schur functions. These coefficients are natural numbers, which the Littlewood–Richardson rule describes as counting certain skew tableaux. They occur in many other mathematical contexts, for instance as multiplicity in the decomposition of tensor products of finite-dimensional representations of general linear groups, or in the decomposition of certain induced representations in the representation theory of the symmetric group, or in the area of algebraic combinatorics dealing with Young tableaux and symmetric polynomials. Littlewood–Richardson coefficients depend on three partitions, say \lambda,\mu,\nu, of which \lambda and \mu describe the Schur functions being multiplied, and \nu gives the Schur function of which this is the coefficient in the linear combination; in other words they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperdeterminant
In algebra, the hyperdeterminant is a generalization of the determinant. Whereas a determinant is a scalar valued function defined on an ''n'' × ''n'' square matrix, a hyperdeterminant is defined on a multidimensional array of numbers or tensor. Like a determinant, the hyperdeterminant is a homogeneous polynomial with integer coefficients in the components of the tensor. Many other properties of determinants generalize in some way to hyperdeterminants, but unlike a determinant, the hyperdeterminant does not have a simple geometric interpretation in terms of volumes. There are at least three definitions of hyperdeterminant. The first was discovered by Arthur Cayley in 1843 presented to the Cambridge Philosophical Society. A. Cayley, "On the theory of determinants", ''Trans. Camb. Philos. Soc.'', 1-16 (1843) https://archive.org/details/collectedmathem01caylgoog It is in two parts and Cayley's first hyperdeterminant is covered in the second part. It is usually denoted by det0. The se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Kapranov
Mikhail Kapranov, (Михаил Михайлович Капранов, born 1962) is a Russian mathematician, specializing in algebraic geometry, representation theory, mathematical physics, and category theory. He is currently a professor of the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo. Kapranov graduated from Lomonosov University in 1982 and received his doctorate in 1988 under the supervision of Yuri Manin at the Steklov Institute in Moscow. Afterwards he worked at the Steklov Institute and from 1990 to 1991 at Cornell University. At Northwestern University he was from 1991 to 1993 an assistant professor, from 1993 to 1995 an associate professor, and from 1995 to 1999 a full professor. He was from 1999 to 2003 a professor at University of Toronto and from 2003 to 2014 a professor at Yale University. In 1993 he was a Sloan Research Fellow. From fall 2018 to spring 2019 he was a visiting professor at the Institute for Advanced Stud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P-adic Group
In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. The extension is achieved by an alternative interpretation of the concept of "closeness" or absolute value. In particular, two -adic numbers are considered to be close when their difference is divisible by a high power of : the higher the power, the closer they are. This property enables -adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory – including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles. These numbers were first described by Kurt Hensel in 1897, though, with hindsight, some of Ernst Kummer's earlier work can be interpreted as implicitly using -adic numbers.Translator's introductionpage 35 "Indeed, with hindsight it becomes apparent that a discret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cluster Algebra
Cluster algebras are a class of commutative rings introduced by . A cluster algebra of rank ''n'' is an integral domain ''A'', together with some subsets of size ''n'' called clusters whose union generates the algebra ''A'' and which satisfy various conditions. Definitions Suppose that ''F'' is an integral domain, such as the field Q(''x''1,...,''x''''n'') of rational functions in ''n'' variables over the rational numbers Q. A cluster of rank ''n'' consists of a set of ''n'' elements of ''F'', usually assumed to be an algebraically independent set of generators of a field extension ''F''. A seed consists of a cluster of ''F'', together with an exchange matrix ''B'' with integer entries ''b''''x'',''y'' indexed by pairs of elements ''x'', ''y'' of the cluster. The matrix is sometimes assumed to be skew-symmetric, so that ''b''''x'',''y'' = –''b''''y'',''x'' for all ''x'' and ''y''. More generally the matrix might be skew-symmetrizable, meaning there are positive integers '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergey Fomin
Sergey Vladimirovich Fomin (Сергей Владимирович Фомин) (born 16 February 1958 in Saint Petersburg, Russia) is a Russian American mathematician who has made important contributions in combinatorics and its relations with algebra, geometry, and representation theory. Together with Andrei Zelevinsky, he introduced cluster algebras. Biography Fomin received his M.Sc in 1979 and his Ph.D in 1982 from St. Petersburg State University under the direction of Anatoly Vershik and Leonid Osipov. Previous to his appointment at the University of Michigan, he held positions at the Massachusetts Institute of Technology from 1992 to 2000, at the St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences, and at the Saint Petersburg Electrotechnical University. Sergey Fomin studied at the 45th Physics-Mathematics School and later taught mathematics there. Research Fomin's contributions include * Discovery (with A. Zelevinsky) of cluster al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tanya Zelevinsky
Tanya Zelevinsky is a professor of physics at Columbia University. Her research focuses on high-precision spectroscopy of cold molecules for fundamental physics measurements, including molecular lattice clocks, ultracold molecule photodissociation, as well as cooling and quantum state manipulation techniques for diatomic molecules with the goal of testing the Standard Model of particle physics. Zelevinsky graduated from MIT in 1999 and received her Ph.D. from Harvard University in 2004 with Gerald Gabrielse as her thesis advisor. Subsequently, she worked as a post-doctoral research associate at the Joint Institute for Laboratory Astrophysics (JILA) with Jun Ye on atomic lattice clocks. She joined Columbia University as an associate professor of physics in 2008. Professor Zelevinsky became a Fellow of the American Physical Society in 2018 and received the Francis M. Pipkin Award in 2019. Research Zelevinsky is known for her pioneering experiments with ultracold strontium, an al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
