I am interested in several areas of Mathematics and Mathematical Physics:
In Okayama (Japan) in 2005
Arithmetic Algebraic Geometry: L-functions, mixed motives and motivic Galois groups, polylogarithms, periods, Hodge Theory, and other topics.
Cluster varieties and Representation theory.
Geometry, Quantum higher Teichmuller theory, Quantum Field Theory.
Integral Geometry and Tomography.
How to reach me
- Department of Mathematics, Yale University,
P.O. Box 208283;
10 Hillhouse ave, New Haven CT 06520
(203) 432-4192 (office)
- Office: 212A LOM
Publications not available in the arXive:
A) Selected publications on zeta-functions, mixed motives, and motivic Galois groups:
The classical trilogarithm, algebraic K-theory of fields, and dedekind zeta functions.
BAMS Vol 24, N1, 1991
Geometry of configurations, polylogarithms and motivic cohomology.
Preprint MPIM (Bonn) 1991. Published in Advances Math. (1995).
Polylogarithms and motivic Galois groups.
Proc. Symp Pure Math vol 55 N 2 (pdf )
Explicit constructions of characteristic classes.
Preprint MPIM (Bonn) 1992
Soviet Mathematics, 16, Volume 1, (dedicated to I.M.Gelfand
80th birthday), 169 - 210, 1993: (pdf )
The classical polylogarithms, algewbraioc K-theory and zeta-values.
The Gelfand mathematical seminars, 1990-1992.
L.Corwin, I.Gelfand, J.Lepowsky edotirs, Birkhauser 1993, 113-161.
The double logarithm and Manin's complexes for modular curves.
Mathematical Research Letters, 4, 617-636 (1997)
Chow polylogarithms and regulators.
Mathematical Research Letters, 2 (1995), no. 1, 95–112.
Mixed elliptic motives.
London Math Soc. Lecture Note Series, Volume 254, 147-221, 1998.
B) Selected Publications in Geometry and Integral Geometry:
Infinitesimal structures related to Hermitian symmetric spaces.
Functional Analysis and its applications, 15, 1981, N3, p 83-84.
Constructions of Weil representations of some simple Lie algebras.
Functional Analysis and its applications, 16, 1982, N2, p 70-71.
Generalized Conformal structures on manifolds
Selecta Mathematica Soveitica 6, (1987) N4, 307-340.
(Russian version: In "Problems in group theory and homological algebra" Yaroslavl Gos. Univ., 1983).
Integral Geometry on families of k-dimensional submanifolds.
Functional Analysis and its applications, 1988, vol 23, N3, p. 11-23. (pdf )
Integral Geometry and manifolds of minimal degree in CP^n.
Functional Analysis and its applications, 1989, vol 24, N1, p. 5-20. (pdf )
Integral Geometry on families of surfaces in the space.
Journal of Geometry and Physics, 1988, vol 4, N5, p. 571-593. (pdf )
Integral geometry and differential equations.
Mathematical Research Letters, 1995, vol 2, N 2, 415-435.
Differential equations and integral geometry.
Math., vol. 131, N2, (1997).
C) Selected Publications in Tomography:
Vainstein B.K., Goncharov A.B.:
Determination of the spatial orientation of arbitrarily arranged
identical particles of unknown structure from their projections.
Doklady Acad. Nauk SSSR, 1986, vol 287, 1131-1134 (April 1986).
English translation: Soviet Physics, Doklady 31(4) April 1986, 278-280.
Goncharov A.B.: Methods of integral geometry and
finding the relative orientation of identical particles arbitrarily
arranged in a plane from their projections onto a straight line.
Doklady Acad. Nauk SSSR, 1987, vol 293, 355-358, (March 1987).
English translation: Soviet Physics, Doklady 32(3) March 1987, 177-178.
Goncharov A.B.: Integral geometry and three dimensional reconstruction of randomly oriented identical particles from their electron micrographs.
Acta Applicanda Mathematicae, 1988, 11, p.199-211. (pdf )
Goncharov A.B.: Methods of integral geometry and recovering a function with compact support from its projections in unknown directions.
Acta Applicanda Mathematicae, 1988, 11, p.213-222. (pdf )