Andrei Zelevinsky

Andrei Vladlenovich Zelevinsky (Андрей Владленович Зелевинский; 30 January 1953 – 10 April 2013)^[1] was a Russian-American mathematician who made important contributions to algebra, combinatorics, and representation theory, among other areas.

Andrei Zelevinsky
Born	(1953-01-30)January 30, 1953 Moscow, Soviet Union
Died	April 10, 2013(2013-04-10) (aged 60) Boston, United States
Nationality	Soviet Union United States
Alma mater	Moscow State University
Known for	Bernstein–Zelevinsky classification Cluster algebras
Awards	Humboldt Prize (2004) Leroy P. Steele Prize (2018)
Scientific career
Fields	Mathematics
Institutions	Northeastern University
Doctoral advisors	Israel Gelfand Alexandre Kirillov

Biography

Zelevinsky graduated in 1969 from the Moscow Mathematical School No. 2.^[2] After winning a silver medal as a member of the USSR team at the International Mathematical Olympiad^[3] 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.^[4]

He worked^[5] 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,^[6] 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.^[7]

Zelevinsky is a relative of the physicists Vladimir Zelevinsky and Tanya Zelevinsky.

Research

Zelevinsky's most notable achievement is the discovery (with Sergey Fomin) of cluster algebras. His other contributions include:

• Bernstein–Zelevinsky classification of representations of p-adic groups;
• introduction (jointly with Israel Gelfand and Mikhail Kapranov) of A-systems of hypergeometric equations (also known as GKZ-systems)^[8] and development of the theory of hyperdeterminants;^[9][10]
• generalization of the Littlewood–Richardson rule and Robinson–Schensted correspondence using the combinatorics of "pictures";
• work (jointly with Arkady Berenstein and Sergey Fomin) on total positivity;
• work (with Sergey Fomin) on the Laurent phenomenon, including its applications to Somos sequences.

Awards and recognition

• Invited lecture at the International Congress of Mathematicians (Berlin, 1998)^[11]
• Humboldt Research Award (2004)
• Fellow (2012) of the American Mathematical Society^[12]
• University Distinguished Professorship (2013) at Northeastern University^[13]
• Steele Prize for Seminal Contribution to Research (2018)^[14]

References

1. News on website for the commutative algebra community
2. "Medal-winning graduates of the Moscow Mathematical School No. 2". Archived from the original on 2013-06-15. Retrieved 2013-04-18.
3. IMO Results
4. A. Zelevinsky at the Mathematics Genealogy Project.
5. A. Zelevinsky's cv Archived April 16, 2013, at the Wayback Machine
6. You failed your math test, comrade Einstein
7. Northeastern University, Math. Dep page Archived May 1, 2013, at the Wayback Machine
8. Israel M. Gelfand, Mikhail M. Kapranov, Andrei 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
9. Gelfand, Israel M.; Mikhail M. Kapranov; Andrei V. Zelevinsky (1994). Discriminants, resultants, and multidimensional determinants. Boston: Birkhäuser. ISBN 0-8176-3660-9.
10. Roberts, David P. (2009). "Review: Discriminants, Resultants, and Multidimensional Determinants, by I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky". Mathematical Association of America. Retrieved 1 Jul 2020.
11. Section "Combinatorics" at ICM'98
12. List of Fellows of the American Mathematical Society
13. Northeastern University, Academic Honors Convocation
14. 2018 Steele Prize for Seminal Contribution to Research in Discrete Mathematics/Logic to Sergey Fomin and Andrei Zelevinsky

External links

• 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 from 2007 to 2013
• Andrei Zelevinsky at the Mathematics Genealogy Project