Joseph Bernstein

Joseph Naumovich Bernstein (Russian Иосиф Н Бернштейн; . Hebrew יוסף ברנשטיין; born April 18, 1945 in Moscow ) is a Russian-born Israeli mathematician who deals with representation theory, algebraic geometry, number theory and automorphic functions.

Bernstein studied at Moscow University in 1963 where he got his degree in 1968 and received his doctorate in 1972 at Israel Gelfand. 1981/82 he was a visiting professor at the University of Maryland, and from 1983 to 1993 professor at Harvard. From 1993 he was a professor at the University of Tel Aviv.

He is co-inventor of concepts such as the Bernstein - Sato polynomials (1971 ) and modules ( modules over a ring of differential operators ) from the algebraic theory of differential equations. With Alexander Beilinson, Deligne and Ofer Gabber he introduced in 1982 the concept of " perverse sheaves " a, an abstract algebraic formalization of ideas from the environment of the ( higher dimensional ) Riemann - Hilbert problem to look for ( differential equations to a given monodromy group, the behavior of the of solutions when running around the singularities determine ), the Riemann - Hilbert correspondence. With Beilinson, Deligne and Gabber he proved to 1982, the decomposition theorem ( decomposition theorem ), the hard Lefschetz theorem and semisimplicity theorem for perverse sheaves (for positive characteristics and existence of a Galois action).

With Alexander Beilinson he proved 1981, the Kazhdan - Lusztig conjectures in geometric representation theory.

With Andrei Zelevinsky he coined the p- adic representations of 1976 groups.

He became a member of the Israel Academy of Sciences and in 2004 the National Academy of Sciences of the United States 2002. In 1976 he was awarded the prize of the Moscow Mathematical Society. In 2004 he was awarded the Israel Prize. In 1998 he was invited speaker at the International Congress of Mathematicians in Berlin ( Analytic structures on representation spaces of reductive groups). He is a Fellow of the American Mathematical Society.

Among his doctoral students include Alexander Braverman, Dennis Gaitsgory and Edward Frenkel.