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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 a ... [...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 alk ... [...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 In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tens .... 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, ... [...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 ... [...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] |
Bernstein–Zelevinsky Classification
In mathematics, the Bernstein–Zelevinsky classification, introduced by and , classifies the irreducible complex smooth representations of a general linear group over a local field in terms of cuspidal representation In number theory, cuspidal representations are certain representations of algebraic groups that occur discretely in L^2 spaces. The term ''cuspidal'' is derived, at a certain distance, from the cusp forms of classical modular form theory. In the co ...s. References * * * * {{DEFAULTSORT:Bernstein-Zelevinsky classification Representation theory ... [...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 St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Israel Gelfand
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand ( yi, ישראל געלפֿאַנד, russian: Изра́иль Моисе́евич Гельфа́нд, uk, Ізраїль Мойсейович Гельфанд; – 5 October 2009) was a prominent Soviet-American mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the first Wolf Prize, he was a Foreign Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University. Gelfand is also a 1994 MacArthur Fellow. His legacy continues through his students, who include Endre Szemerédi, Alexandre Kirillov, Edward Frenkel, Joseph Bernstein, David Kazhdan, as well as his own son, Sergei Gelfand. Early years A native of Kherson G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jewish People's University
Jewish People's University – unofficial semi-underground mathematical courses in Moscow in 1978–1982. History of creation The idea of creating a People's University came about by interviewing applicants MSU Faculty of Mechanics and Mathematics (Mekhmat) who did not pass the selection committee, primarily due to their Jewish origin , from mathematicians Bella Subbotovskaya and Valery Senderov. The first stream was recruited in 1978 directly at Moscow State University and amounted to 14 people. Classes were held at Bella Abramovna's apartment. The sets of 1979 – 1981 and exceeded 100 people, not all of whom, however, remained after the first year: for example, out of more than 120 people recruited in 1980 , about 60 remained. This is due to both the very high level of difficulty of the material taught and the fact that students were forced to study at other institutes at the same time and not everyone could withstand this pace. Classes were held in various classrooms thr ... [...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. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Picture (mathematics)
In combinatorial mathematics, a picture is a bijection between skew diagrams satisfying certain properties, introduced by in a generalization of the Robinson–Schensted correspondence and the 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 numbe .... 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] |
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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
