January 30, 1953|
Moscow, Soviet Union
|Died||April 10, 2013
Boston, United States
|Alma mater||Moscow State University|
|Doctoral advisors||Israil Gelfand, Alexandre Kirillov|
|Doctoral students||Arkady Berenstein
Giovanni Cerulli Irelli
|Known for||Bernstein-Zelevinsky classification, Cluster algebras|
Andrei Vladlenovich Zelevinsky (Андрей Владленович Зелевинский; 30 January 1953 – 10 April 2013) was a Russian-American mathematician who made important contributions to algebra, combinatorics, and representation theory, among other areas.
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 Peoples' University, 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, and from 1991 until his death was on faculty at Northeastern University, Boston. With his wife, Galina, he had a son and a daughter; he also had several grandchildren.
Zelevinsky's contributions include:
- Bernstein–Zelevinsky classification of representations of p-adic groups;
- introduction (jointly with I. Gelfand and M. Kapranov) of A-systems of hypergeometric equations (also known as GKZ-systems) and development of the theory of hyperdeterminants
- generalization of Littlewood–Richardson rule and Robinson-Schensted correspondence using combinatorics of "pictures";
- work (jointly with A. Berenstein and S. Fomin) on total positivity;
- work (with S. Fomin) on the Laurent phenomenon, including its applications to Somos sequences;
- discovery (with S. Fomin) of cluster algebras.
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 University
- News on website for the commutative algebra community
- Medal-winning graduates of the Moscow Mathematical School No. 2
- IMO Results
- A. Zelevinsky at the Mathematics Genealogy Project.
- A. Zelevinsky's cv
- You failed your math test, comrade Einstein
- Northeastern University, Math. Dep page
- I. M. Gelfand, M. M. Kapranov, A. V. Zelevinsky, Hypergeometric functions and toric varieties, (Russian) Funktsional. Anal. i Prilozhen. 23 (1989), no. 2, 12–26; translation in Funct. Anal. Appl. 23 (1989), no. 2, 94–10
- Gelfand, I. M.; M.M. Kapranov; A.V. Zelevinsky (1994). Discriminants, resultants, and multidimensional determinants. Boston: Birkhäuser. ISBN 0-8176-3660-9.
- Section "Combinatorics" at ICM'98
- List of Fellows of the American Mathematical Society
- Northeastern University, Academic Honors Convocation
- Home page of Andrei Zelevinsky (including CV)
- Conference in memory of Andrei Zelevinsky
- Publications of Andrei Zelevinsky (In Russian)
- Publications of Andrei Zelevinsky (In English)
- Research Focus: Andrei Zelevinsky's Cluster Algebras
- Live journal run by Andrei Zelevinsky in 2007-13
- A. Zelevinsky at the Mathematics Genealogy Project