Alexander Goncharov

Alexander B. Goncharov ( born April 7, 1960) is a Ukrainian- American mathematician who, arithmetic algebraic geometry and geometry works in algebraic geometry.

Life

Goncharov was awarded in 1976 to the Mathematical Olympiad gold medal. He studied at the Moscow State University in Moscow, where he attended the seminars of Israel Gelfand, Alexander Beilinson and Yuri Manin. In 1982 he received his degree. 1985 to 1992 he was at the group of Cybernetics of the Academy of Sciences of the USSR in Moscow. In 1987, he was there in Israel Gelfand PhD ( " Generalized conformal structures on manifolds" ). In 1990 he went to the USA. In 1991, he was Harvard Prize Fellow at Harvard University, 1992/3 at the MSRI ( and 2001 ), 1990 and 1992, a visiting scientist at MIT, where he was a Lecturer from 1993 to 1995. 1996 to 1998 he was a professor at the Max Planck Institute for Mathematics in Bonn and at the same time from 1996 associate professor at Brown University. In 1999 he became a professor at Brown University, he is since 2010 professor at Yale University, but is a regular guest scientists in Europe ( Max - Planck - Institute for Mathematics in Bonn, Institut des Hautes Études Scientifiques in Paris).

He worked on the theory of motives and polylogarithms in connection with the study of motivic fundamental groups of algebraic curves. Here he found a connection between the motivic fundamental groups of the projective line without zero, the point at infinity and the N- th roots of unity and the geometry of modular varieties for the linear group GL (N ) for all N. He also found correlations between the motivic fundamental groups and Feynman integrals in quantum field theory. He proved special cases of Don Zagier 's conjecture about the relationship between polylogarithms and values ​​of Dedekind zeta function at specific integer points and extended these to follow named him conjecture ( conjecture of Goncharov ), the relationships between algebraic K- theory and cohomology of motivic complexes socialize.

He was also higher Teichmüller theory and its quantization, as well as with integral geometry.

In 1992 he was awarded the EMS price of European mathematicians company on the First European Congress of Mathematicians in Paris. In 1994 he was invited speaker at the International Congress of Mathematicians ( " Polylogarithms in arithmetic and geometry ").

Works (selection)

  • Geometry of configurations, polylogarithms, and motivic cohomology. Adv Math 114 (1995), no 2, 197-318.
  • ( with A. M. Levin ) Zagier 's conjecture on L (E, 2). Invent. Math 132 (1998), no 2, 393-432.
  • (with P. Deligne ) Groupes de fondamentaux motiviques Tate mixte. Ann. Sci. École standard. Sup ( 4) 38 (2005 ), no 1, 1-56.
  • ( with VV Fock ) moduli spaces of local systems and higher Teichmüller theory. Publ Math Inst Hautes Études Sci. No. 103 (2006), 1-211.
  • ( with VV Fock ) The quantum dilogarithm and representations of quantum cluster varieties. Invent. Math 175 (2009), no 2, 223-286.
  • ( with H. Gangl, A. Levin ) Multiple logarithms, algebraic cycles and trees, in Pierre Cartier, among others Frontiers in Number Theory, Physics and Geometry, Volume 2, Springer Verlag 2007
Russian Academy of Sciences Mathematics Genealogy Project
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