Alexander Goncharov

I am interested in several areas of Mathematics and Mathematical Physics:

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

Contact

Department of Mathematics, Yale University
P.O. Box 208283;
219 Prospect street, New Haven CT 06520
10 Hillhouse Ave, New Haven, CT 06520
USA

Email: alexander.goncharov@yale.edu

Phone: (203) 432-4192

Office: 717 Klain Tower, New Haven CT 06511, USA

In Okayama, Japan (2005)

Polylogarithms in arithmetic and geometry
International Congress of Mathematicians, Zurich, 1994 PDF
Multiple zeta-values, Galois groups and geometry of modular varieties
European Congress of Mathematicians, Barcelona, 2000 PDF
Galois groups, geometry of modular varieties, and graphs
Arbeitstagung, Bonn, 1999 PDF
Hidden Hodge symmetries and Hodge correlators
Arbeitstagung, Bonn, 2011 PDF

Quantum geometry of moduli spaces of local systems and representation theory
With L. Shen arXiv:1904.10491
Spectral description of non-commutative local systems on surfaces and non-commutative cluster varieties
With M. Kontsevich arXiv:2108.04168
Exponential complexes, period morphisms, and characteristic classes
With D. Rudenko arXiv:2212.04194
Motivic correlators, cluster varieties, and Zagier's conjecture on ζ_F(4)
With O. Kislinskyi arXiv:2105.06295
Geometry of canonical bases and mirror symmetry
With L. Shen arXiv:1309.5922
The Galois group of the category of mixed Hodge-Tate structures
With G. Zhu arXiv:1705.08175
Dimers and cluster integrable systems
With R. Kenyon, Annales Scientifiques de l'École Normale Supérieure arXiv:1107.5588
Moduli spaces of local systems and higher Teichmüller theory
With V. Fock, Publications Mathématiques de l'IHÉS arXiv:math/0311149
Cluster ensembles, quantization and the dilogarithm
With V. Fock, Annales Scientifiques de l'École Normale Supérieure arXiv:math/0311245
Groupes fondamentaux motiviques de Tate mixte
With P. Deligne, Annales Scientifiques de l'École Normale Supérieure arXiv:math/0302267

Note: The following publications are not available on the arXiv. PDF files are provided where available.

The classical trilogarithm, algebraic K-theory of fields, and Dedekind zeta functions
BAMS Vol 24, N1, 1991 PDF
Geometry of configurations, polylogarithms and motivic cohomology
Preprint MPIM (Bonn) 1991. Published in Advances Math. (1995) PDF
Polylogarithms and motivic Galois groups
Proc. Symp Pure Math vol 55 N 2 PDF
Explicit constructions of characteristic classes
Preprint MPIM (Bonn) 1992 PDF
Advances in Soviet Mathematics, 16, Volume 1, (dedicated to I.M. Gelfand 80th birthday), 169-210, 1993 PDF
The classical polylogarithms, algebraic K-theory and zeta-values
The Gelfand mathematical seminars, 1990-1992. L. Corwin, I. Gelfand, J. Lepowsky editors, Birkhäuser 1993, 113-161 PDF
The double logarithm and Manin's complexes for modular curves
Mathematical Research Letters, 4, 617-636 (1997) PDF
Chow polylogarithms and regulators
Mathematical Research Letters, 2 (1995), no. 1, 95–112 PDF
Mixed elliptic motives
London Math Soc. Lecture Note Series, Volume 254, 147-221, 1998 PDF

Infinitesimal structures related to Hermitian symmetric spaces
Functional Analysis and its applications, 15, 1981, N3, p 83-84 PDF
Constructions of Weil representations of some simple Lie algebras
Functional Analysis and its applications, 16, 1982, N2, p 70-71 PDF
Generalized Conformal structures on manifolds
Selecta Mathematica Sovietica 6, (1987) N4, 307-340 PDF
(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 PDF
Differential equations and integral geometry
Advances in Math., vol. 131, N2, (1997) PDF

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 PDF
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 PDF
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