Joseph Bernstein

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Joseph Bernstein (2005)

Joseph Naumowitsch Bernstein ( Russian Иосиф Наумович Бернштейн ; Hebrew יוסף ברנשטיין; *  April 18, 1945 in Moscow ) is an Israeli mathematician born in Russia who specializes in representation theory , algebraic geometry , automorphic functions, and number theory.

Career

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

He is co-inventor of concepts like the Bernstein-Sato polynomials (1971) and modules (modules over a ring of differential operators) from the algebraic theory of differential equations. With Alexander Beilinson , Pierre Deligne and Ofer Gabber , he introduced the concept of " perverse sheaves " in 1982 , an abstract algebraic formalization of ideas from the environment of the (higher-dimensional) Riemann-Hilbert problem (differential equations for a given monodromic group that search for behavior of the solutions while circulating the singularities), the Riemann-Hilbert correspondence . With Beilinson, Deligne and Gabber around 1982 he proved the decomposition theorem , the difficult Lefschetz theorem and semi-simplicity theorem for perverse sheaves (for positive characteristics and existence of a Galois group effect).

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

With Andrei Zelevinsky he classified representations of p-adic groups in 1976 .

In 2002 he became a member of the Israel Academy of Sciences and in 2004 the National Academy of Sciences of the United States. In 1976 he received the Moscow Mathematical Society Prize. In 2004 he received 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 .

His PhD students include Alexander Braverman , Dennis Gaitsgory and Edward Frenkel .

Web links

Individual evidence

  1. ↑ Independent of Masaki Kashiwara in Japan
  2. ↑ Alexander A. Beilinson , J. Bernstein, Pierre Deligne : Faisceaux pervers (= Analyze et Topologie sur les Espaces Singuliers. CIRM, 6-10 June 1981. 1 = Asterisque. 100, ISSN  0303-1179 ). Société Mathématique de France, Paris 1982, ( digitized , French).
  3. ^ Mark Andrea A. de Cataldo , Luca Migliorini : The Hodge Theory of Algebraic Maps. In: Annales scientifiques de l'École normal supérieure . Series 4, Volume 38, No. 5, 2005, pp. 693-750, doi : 10.1016 / j.ansens.2005.07.001 .
personal data
SURNAME Bernstein, Joseph
ALTERNATIVE NAMES Bernstein, Joseph Naumowitsch (full name); Бернштейн, Иосиф Наумович (Russian); יוסף ברנשטיין (Hebrew)
BRIEF DESCRIPTION Israeli mathematician
DATE OF BIRTH April 18, 1945
PLACE OF BIRTH Moscow