About

Alexander Goncharov is the Philip Schuyler Beebe Professor of Mathematics at Yale University. His research areas include Arithmetic, Algebraic Geometry, Geometry, Representation Theory, and Mathematical Physics. Professor Goncharov holds a Ph.D. obtained in 1987 in the USSR. His work is recognized within the mathematical community, and he has received notable awards such as the European Mathematical Society Prize. He is a member of Yale's faculty of Arts and Sciences, contributing to the department's academic and research activities. His contact information includes an email address at alexander.goncharov@yale.edu and a phone number +1 (203) 432-4192, with office location at Kline Tower 219, Prospect Street, New Haven, CT.

Research topics

• Computer Science
• Political Science
• Physics
• Geometry
• Engineering
• Mathematics
• Pure mathematics
• Mathematical analysis
• Computational chemistry
• Chemistry
• Nuclear magnetic resonance
• Theoretical physics

Selected publications

• Lebesgue constants for Cantor sets. Numerical results

  Journal of Numerical Analysis and Approximation Theory · 2025-06-30

  articleOpen access1st authorCorresponding

  We analyze numerically the form of Lebesgue functions and the values of Lebesgue constants in polynomial interpolation for three types of Cantor sets.

  PublisherOA PDFDOI

• Bases and Isomorphisms of Whitney Spaces

  Approximation Theory and Special Functions · 2025-10-16

  articleOpen access1st authorCorresponding

  We consider results related to bases and isomorphisms of Whitney spaces E(K) and the extension property of compact sets K. The first two sections discuss the notion of a topological basis and its importance in analysis. Then we consider model spaces of infinitely differentiable functions that may occur in applications. Our main interest is in Whitney spaces E(K) and the extension property of compact sets, that is, the existence of a continuous linear extension operator from E(K) to the space of infinitely differentiable functions on the whole Euclidean space. In Section 5 we consider what we believe to be the main methods for constructing such an operator. Section 6 contains some geometric and other conditions characterizing the extension property. Sections 7-11 are devoted to bases in spaces of infinitely differentiable functions, Whitney spaces, and restriction spaces, with an emphasis on the author's results obtained using the method of local interpolations. The final sections present results related to the isomorphic classification of these spaces. We consider the counting linear topological invariants (mainly the diametrical dimension), interpolation invariants (mainly generalizations of the dominated norm property), and compound invariants, which reduce to the computation of diametrical dimension for so-called synthetic neighborhoods. Various families of the continuum cardinality of pairwise non-isomorphic spaces are presented. Finally, some open problems are proposed. The review contains many examples, both classic and new.

  PublisherDOI

• Lebesgue Constants for Cantor Sets

  Experimental Mathematics · 2024-08-18

  article1st author

  We evaluate the values of the Lebesgue constants in polynomial interpolation for three types of Cantor sets. In all cases, the sequences of Lebesgue constants are not bounded. This disproves the statement by Mergelyan.

  PublisherDOI

• The Inverse Spectral Map for Dimers

  Mathematical Physics Analysis and Geometry · 2023 · 4 citations

  • Computer Science
  • Mathematics
  • Pure mathematics
  PublisherDOI

• Memorial Article for Yuri Manin

  Notices of the American Mathematical Society · 2023

  • Computer Science
  • Computer Science

  Yuri Manin was

  PublisherDOI

• Bases in the spaces of Whitney jets

  Banach Journal of Mathematical Analysis · 2022-01-01 · 3 citations

  articleOpen access1st authorCorresponding
  PublisherOA PDFDOI

• Lebesgue Constants For Cantor Sets

  arXiv (Cornell University) · 2021-01-01

  preprintOpen access1st authorCorresponding

  We evaluate the values of the Lebesgue constants in polynomial interpolation for three types of Cantor sets. In all cases, the sequences of Lebesgue constants are not bounded. This disproves the statement by Mergelyan.

  PublisherOA PDFDOI

• Classifications of intratextual relations: Bases and structuring principles

  Voprosy Jazykoznanija · 2021

  1st authorCorresponding
  • Political Science
  • Physics
  • Theoretical physics
  DOI

• Logarithmic dimension and bases in Whitney spaces

  TURKISH JOURNAL OF MATHEMATICS · 2021-05-04

  articleOpen access1st authorCorresponding

  We give a formula for the logarithmic dimension of the generalized Cantor-type set K. In the case when the logarithmic dimension of K is smaller than 1, we construct a Faber basis in the space of Whitney functions ε(K).

  PublisherDOI

• Quasi-equivalence of bases in some Whitney spaces

  Canadian Mathematical Bulletin · 2021-05-18 · 4 citations

  articleOpen access1st authorCorresponding

  Abstract If the logarithmic dimension of a Cantor-type set K is smaller than $1$ , then the Whitney space $\mathcal {E}(K)$ possesses an interpolating Faber basis. For any generalized Cantor-type set K , a basis in $\mathcal {E}(K)$ can be presented by means of functions that are polynomials locally. This gives a plenty of bases in each space $\mathcal {E}(K)$ . We show that these bases are quasi-equivalent.

  PublisherOA PDFDOI

Recent grants

• Polylogarithms, Moduli Spaces, Mixed Motives, and L-Functions

  NSF · $150k · 2004–2008

• Moduli Spaces, Motives, Periods, and Scattering Amplitudes

  NSF · $194k · 2016–2019

• Polylogarithms, Moduli Spaces, Mixed Motives and L-Functions

  NSF · $199k · 2007–2010

• Polylogarithms, moduli spaces, Hodge theory, motives and L-functions

  NSF · $236k · 2010–2013

• MODULI SPACES, MOTIVES, PERIODS and SCATTERING AMPLITUDES

  NSF · $306k · 2013–2016

Frequent coauthors

• V. V. Fock

  Institut de Recherche Mathématique Avancée

  32 shared

• Anastasia Volovich

  6 shared

• A. Levin

  Siberian Research Institute of Agriculture and Peat

  6 shared

• Marcus Spradlin

  6 shared

• Cristian Vergu

  University of Copenhagen

  5 shared

• Linhui Shen

  Michigan State University

  5 shared

• Yu. I. Manin

  Max Planck Institute for Mathematics

  5 shared

• Jacob L. Bourjaily

  Pennsylvania State University

  4 shared

Education

• Ph.D., Mathematics

  Rostov State University Faculty of Mechanics and Mathematics