Alexander Beilinson

Alexander Beilinson ( born June 13, 1957) is a Russian mathematician who deals with arithmetic and algebraic geometry, representation theory and mathematical physics.

Life and work

Beilinson studied in Moscow, where he received his doctorate at Yuri Manin. 1980 to 1988 he was a research mathematician at a cardiology center in Moscow. 1989 to 1998 he taught in the fall at the Massachusetts Institute of Technology (MIT) and was also a scientist at the Landau Institute for Theoretical Physics in Chernogolovka in Russia. Since 1998 he is " David and Mary Winton Green" Professor of Mathematics at the University of Chicago, where Spencer Bloch taught, with whom he worked closely.

In the representation theory he proved with Joseph Bernstein 1981, the Kazhdan - Lusztig conjectures, the methods used in the proof were influential in the development of the geometric representation theory. With Bernstein, Deligne and Gabber Ofer he led perverse sheaves and proved for this to 1982, the decomposition theorem, the hard Lefschetz theorem and a semisimplicity theorem (for positive characteristics and existence of a Galois action).

In 1982, he published a letter to Soulé conjecture about the existence of a motivic cohomology of schemes and algebraic varieties. The suspicions have been realized in the 1990s in the program of Vladimir and Andrei Suslin Wojewodski for construction of such motivic cohomology theories partially.

In 1984 he formulated in Higher Regulators and Values ​​of- functions, the groundbreaking for the further development of arithmetic algebraic geometry Beilinson conjectures that the leading terms of the Taylor expansion of the functions of algebraic varieties at integer points with the groups and the Deligne - Beilinson - set cohomology of the variety combined. They also include a number of well known senior assumptions such as the Tate conjecture on algebraic cycles and the conjecture of Birch and Swinnerton - Dyer for elliptic curves.

With Vladimir Drinfeld, which is also at the University of Chicago, and he knew from Moscow, he worked on a reformulation of the theory of Vertexalgebren, which was released in 2004 as a book Chiral Algebras ( AMS), the applications in string theory and have conformal field theory.

In 1984 he received the mathematics prize of the Moscow Mathematical Society. In 2008 he was inducted into the American Academy of Arts and Sciences. In 1999 he was awarded the Ostrowski Prize. In 1983 he was invited speaker at the International Congress of Mathematicians in Warsaw ( Localization of representations of reductive Lie algebras ).