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Andrei Zelevinsky

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Name
  
Andrei Zelevinsky

Fields
  
Mathematics


Andrei Zelevinsky mathserverneueduzelevinskyandrei032312jpg

Born
  
January 30, 1953 Moscow, Soviet Union (
1953-01-30
)

Nationality
  
Soviet Union United States

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

Died
  
April 10, 2013, Boston, Massachusetts, United States

Books
  
Discriminants, Resultants, and Multidimensional Determinants

Academic advisor
  
Israel Gelfand, Alexandre Kirillov

Education
  
Moscow State University

Andrei zelevinsky cluster algebras via quivers with potentials


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.

Contents

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 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.

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) 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

    • References

    Andrei Zelevinsky Wikipedia
    (Text) CC BY-SA