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Mathematics

D-Index
40
Citations
11848
World Ranking
1991
National Ranking
31

Overview

Mikhail Kapranov is affiliated with the Kavli Institute for the Physics and Mathematics of the Universe in Japan. Their academic work predominantly focuses on the field of Mathematics, with significant contributions to Geometry and Topology, Mathematical Physics, Algebra and Number Theory, Discrete Mathematics and Combinatorics, and Nuclear and High Energy Physics.

The main topics of their research include:

  • Algebraic structures and combinatorial models
  • Homotopy and Cohomology in Algebraic Topology
  • Advanced Algebra and Geometry
  • Algebraic Geometry and Number Theory
  • Advanced Topics in Algebra
  • Advanced Combinatorial Mathematics
  • Black Holes and Theoretical Physics

Mikhail Kapranov has published extensively, with 59 publications in Mathematics. Their frequent publication venues include:

  • arXiv (Cornell University)
  • Journal of the European Mathematical Society
  • Journal of the American Mathematical Society
  • Pure and Applied Mathematics Quarterly
  • Publications of the Research Institute for Mathematical Sciences

Recent papers highlight the breadth of their research:

  • The cohomological Hall algebra of a surface and factorization cohomology (2022), Journal of the European Mathematical Society
  • Gel'fand-Fuchs cohomology in algebraic geometry and factorization algebras (2022), Journal of the American Mathematical Society
  • Shuffle algebras and perverse sheaves (2020), Pure and Applied Mathematics Quarterly
  • Perverse Sheaves over Real Hyperplane Arrangements II (2022), Publications of the Research Institute for Mathematical Sciences
  • Infinite-dimensional (dg) Lie algebras and factorization algebras in algebraic geometry (2021), Japanese Journal of Mathematics

Collaboration is a notable aspect of Kapranov's work, with frequent coauthors including:

  • Vadim Schechtman
  • Yan Soibelman
  • Tobias Dyckerhoff
  • Éric Vasserot
  • Benjamin Hennion

Best Publications

  • Discriminants, Resultants, and Multidimensional Determinants

    Izrailʹ Moiseevich Gelʹfand;M. M. Kapranov;Andrey V. Zelevinsky

  • Koszul duality for operads

    Victor Ginzburg;Mikhail Kapranov

  • ENHANCED TRIANGULATED CATEGORIES

    A I Bondal;M M Kapranov

  • Non-archimedean amoebas and tropical varieties

    Manfred Einsiedler;Mikhail Kapranov;Douglas Lind

  • On the derived categories of coherent sheaves on some homogeneous spaces

    Unknown

  • REPRESENTABLE FUNCTORS, SERRE FUNCTORS, AND MUTATIONS

    Unknown

  • Kleinian singularities, derived categories and Hall algebras

    M. Kapranov;E. Vasserot

  • Chow quotients of Grassmannian I

    Unknown

  • Hypergeometric functions and toral manifolds

    Unknown

  • Langlands Reciprocity for Algebraic Surfaces

    Victor Ginzburg;Mikhail Kapranov;Eric Vasserot

  • Quotients of toric varieties

    M. M. Kapranov;B. Sturmfels;A. V. Zelevinsky

  • The permutoassociahedron, Mac Lane's coherence theorem and asymptotic zones for the KZ equation

    Mikhail M. Kapranov

  • Derived quot schemes

    Ionuţ Ciocan-Fontanine;Mikhail Kapranov

  • Higher Segal Spaces

    Tobias Dyckerhoff;Mikhail Kapranov

  • Chow polytopes and general resultants

    M. M. Kapranov;B. Sturmfels;A. V. Zelevinsky

  • Eisenstein series and quantum affine algebras

    Unknown

  • NONCOMMUTATIVE GEOMETRY BASED ON COMMUTATOR EXPANSIONS

    Mikhail Kapranov

  • Representation and character theory in 2-categories

    Nora Ganter;Mikhail Kapranov

  • Virtual fundamental classes via dg-manifolds

    Ionuţ Ciocan-Fontanine;Mikhail Kapranov

  • Braided monoidal 2-categories and Manin-Schechtman higher braid groups

    M. Kapranov;V. Voevodsky

  • Vertex algebras and the formal loop space

    Mikhail Kapranov;Eric Vasserot

  • Cellular strings on polytopes

    L. J. Billera;M. M. Kapranov;B. Sturmfels

  • Arrangements of hyperplanes and vector bundles on $P^n$

    Unknown

  • Combinatorial-geometric aspects of polycategory theory : pasting schemes and higher Bruhat orders (list of results)

    M. M. Kapranov;V. A. Voevodsky

  • Elliptic Algebras and Equivariant Elliptic Cohomology

    Victor Ginzburg;Mikhail Kapranov;Eric Vasserot

  • Geometry and Dynamics of Groups and Spaces

    Mikhail Kapranov;Yuri Ivanovich Manin;Pieter Moree;Sergiy Kolyada

Frequent Co-Authors

Andrei Zelevinsky
Andrei Zelevinsky Northeastern University
Victor Ginzburg
Victor Ginzburg University of Chicago
Vladimir Voevodsky
Vladimir Voevodsky Institute for Advanced Study
Bernd Sturmfels
Bernd Sturmfels Max Planck Institute for Mathematics in the Sciences
Maxim Kontsevich
Maxim Kontsevich Institut des Hautes Études Scientifiques
Yuri I. Manin
Yuri I. Manin Max Planck Institute for Mathematics
Ezra Getzler
Ezra Getzler Northwestern University
Louis J. Billera
Louis J. Billera Cornell University
Michael Finkelberg
Michael Finkelberg National Research University Higher School of Economics

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