Andrei Vladlenovich Zelevinsky (; 30 January 1953 – 10 April 2013) was a Russian-American mathematician who made important contributions to

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

, and

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

, 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 The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except i ...

he was admitted without examination to the mathematics department of

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

where he obtained his PhD in 1978 under the mentorship of

Joseph Bernstein Joseph Bernstein (sometimes spelled I. N. Bernshtein; he, יוס(י)ף נאומוביץ ברנשטיין; russian: Иосиф Наумович Бернштейн; born 18 April 1945) is a Soviet-born Israeli mathematician working at Tel Aviv Univ ...

Alexandre Kirillov Alexandre Aleksandrovich Kirillov (russian: Алекса́ндр Алекса́ндрович Кири́ллов, born 1936) is a Soviet and Russian mathematician, known for his works in the fields of representation theory, topological groups a ...

and

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 Гел� ...

. He worked in the mathematical laboratory of

Vladimir Keilis-Borok Vladimir Isaacovich Keilis-Borok (July 31, 1921 – October 19, 2013) was a Russian mathematical geophysicist and seismologist. Biography Keilis-Borok was born in Moscow, Russia. His father, Isaak Moiseevich Keilis, was a jeweler. His mother, ...

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 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 Mathemat ...

, an unofficial organization offering first-class mathematics education to talented students denied admission to Moscow State University's math department. In 1990–91, Zelevinsky was a visiting professor at

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...

, and from 1991 until his death was on faculty at

Northeastern University Northeastern University (NU) is a private university, private research university with its main campus in Boston. Established in 1898, the university offers undergraduate and graduate programs on its main campus as well as satellite campuses in ...

, Boston. With his wife, Galina, he had a son and a daughter; he also had several grandchildren. Zelevinsky is a relative of the physicists

Vladimir Zelevinsky Vladimir may refer to: Names * Vladimir (name) for the Bulgarian, Croatian, Czech, Macedonian, Romanian, Russian, Serbian, Slovak and Slovenian spellings of a Slavic name * Uladzimir for the Belarusian version of the name * Volodymyr for the Ukra ...

and

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 photodissociatio ...

Research

Zelevinsky's most notable achievement is the discovery (with

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 al ...

) of

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 variou ...

s. His other contributions include: *

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 representations. References

* * * * ...

of representations of ''p''-adic groups; * introduction (jointly with

and

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 ...

) of A-systems of hypergeometric equations (also known as GKZ-systems) and development of the theory of

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. ...

s; * generalization of 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 number ...

and

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 remar ...

using the combinatorics of "pictures"; * work (jointly with

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: *Ark ...

and

) on

total positivity In mathematics, a totally positive matrix is a square matrix in which all the minors are positive: that is, the determinant of every square submatrix is a positive number. A totally positive matrix has all entries positive, so it is also a posit ...

; * work (with Sergey Fomin) on the

Laurent Laurent may refer to: *Laurent (name), a French masculine given name and a surname **Saint Laurence (aka: Saint ''Laurent''), the martyr Laurent **Pierre Alphonse Laurent, mathematician **Joseph Jean Pierre Laurent, amateur astronomer, discoverer ...

phenomenon, including its applications to

Somos sequence In mathematics, a Somos sequence is a sequence of numbers defined by a certain recurrence relation, described below. They were discovered by mathematician Michael Somos. From the form of their defining recurrence (which involves division), one wou ...

Awards and recognition

* Invited lecture at the International Congress of Mathematicians (Berlin, 1998) * Humboldt Research Award (2004) * Fellow (2012) of the American Mathematical Society * University Distinguished Professorship (2013) at Northeastern UniversityNortheastern University, Math. Dep page
/ref>--> * Steele Prize for Seminal Contribution to Research (2018)2018 Steele Prize for Seminal Contribution to Research in Discrete Mathematics/Logic to Sergey Fomin and Andrei Zelevinsky
/ref>

References

External links

(includin

Publications of Andrei Zelevinsky (in Russian)Research Focus: Andrei Zelevinsky's Cluster AlgebrasLive journal run by Andrei Zelevinsky from 2007 to 2013
* {{DEFAULTSORT:Zelevinsky, Andrei 20th-century American mathematicians 21st-century American mathematicians Russian mathematicians Northeastern University faculty Fellows of the American Mathematical Society 1953 births 2013 deaths International Mathematical Olympiad participants Soviet mathematicians Combinatorialists