# Andrei Zelevinsky

Andrei Zelevinsky | |
---|---|

Born |
Moscow, Soviet Union | January 30, 1953

Died |
April 10, 2013 Boston, United States |

Nationality |
Soviet Union United States |

Fields | Mathematics |

Institutions | Northeastern University |

Alma mater | Moscow State University |

Doctoral advisors | Israil Gelfand, Alexandre Kirillov |

Doctoral students |
Arkady Berenstein Giovanni Cerulli Irelli Sachin Gautam Oleg Gleizer Daniel Labardini-Fragoso Jeanne Scott Ahmet Seven Salvatore Stella Thao Tran Shih-Wei Yang |

Known for | Bernstein-Zelevinsky classification, Cluster algebras |

**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.

## 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 Peoples' 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]}

## Research

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)
^{[8]}and development of the theory of hyperdeterminants^{[9]} - 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)
^{[10]} - Humboldt Research Award (2004)
- Fellow (2012) of the American Mathematical Society
^{[11]} - University Distinguished Professorship (2013) at Northeastern University
^{[12]}

## References

- ↑ 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 Archived April 16, 2013, at the Wayback Machine.
- ↑ You failed your math test, comrade Einstein
- ↑ Northeastern University, Math. Dep page Archived May 1, 2013, at the Wayback Machine.
- ↑ 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

## 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 in 2007-13
- A. Zelevinsky at the Mathematics Genealogy Project