Andrei Vladlenovich Zelevinsky was a Russian-American mathematician who made important contributions to algebra, combinatorics, and representation theory, among other areas.
Education
Zelevinsky graduated in 1969 from the Moscow Mathematical School Number. After winning a silver medal as a member of the Union of the Soviet Socialist Republics team at the International Mathematical Olympiad he was admitted without examination to the mathematics department of Moscow State University where he obtained his Doctor of Philosophy in 1978 under the mentorship of Joseph Bernstein, Alexandre Kirillov and Israel Gelfand.
Career
2. He worked in the mathematical laboratory of Vladimir Keilis-Borok at the Institute of Earth Science (1977-1985), and at the Council for Cybernetics of the Soviet Academy of Sciences (1985-1990). 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 1990-1991, Zelevinsky was a visiting professor at Cornell University, and from 1991 until his death was on faculty at Northeastern University, Boston.
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 South Fomin) on total positivity.
Work (with South Fomin) on the Laurent phenomenon, including its applications to Somos sequences. Discovery (with South Fomin) of cluster algebras.
Membership
American Mathematical Society.