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Mathematics

D-Index
39
Citations
9756
World Ranking
2135
National Ranking
905

Overview

Mikhail Khovanov is affiliated with Columbia University in the United States and has contributed extensively to the field of mathematics. Their research broadly spans multiple subfields, including Geometry and Topology, Mathematical Physics, Algebra and Number Theory, Computational Theory and Mathematics, and Discrete Mathematics and Combinatorics.

Their main areas of study reflect these subfields, with notable focus on subjects such as Homotopy and Cohomology in Algebraic Topology, Algebraic structures and combinatorial models, Geometric and Algebraic Topology, Advanced Topics in Algebra, Advanced Combinatorial Mathematics, semigroups and automata theory, and Topological and Geometric Data Analysis.

Khovanov's publication record includes a variety of papers appearing in both specialized and broad mathematical venues. Frequent venues for their work include arXiv (Cornell University), Contemporary mathematics - American Mathematical Society, Fundamenta Mathematicae, Letters in Mathematical Physics, and Journal of Pure and Applied Algebra.

Selected papers by Mikhail Khovanov include:

  • Link homology and Frobenius extensions II (2021, Fundamenta Mathematicae)
  • Two-dimensional topological theories, rational functions and their tensor envelopes (2022, Selecta Mathematica)
  • A Faithful Braid Group Action on the Stable Category of Tricomplexes (2020, Symmetry Integrability and Geometry Methods and Applications)
  • Bilinear pairings on two-dimensional cobordisms and generalizations of the Deligne category (2023, Fundamenta Mathematicae)
  • A deformation of Robert-Wagner foam evaluation and link homology (2024, Contemporary mathematics - American Mathematical Society)

Collaboration has been an important aspect of Khovanov's scientific work. Frequent coauthors include Mee Seong Im, Louis-Hadrien Robert, Victor Ostrik, Radmila Sazdanović, and Paul Gustafson, reflecting a network of partnerships across related research topics.

Best Publications

  • A categorification of the Jones polynomial

    Mikhail Khovanov

  • A diagrammatic approach to categorification of quantum groups II

    Mikhail Khovanov;Aaron D. Lauda

  • Matrix factorizations and link homology

    Mikhail Khovanov;Lev Rozansky

  • Quivers, Floer cohomology, and braid group actions

    Mikhail Khovanov;Paul Seidel

  • A functor-valued invariant of tangles

    Mikhail Khovanov

  • Matrix factorizations and link homology II

    Mikhail Khovanov;Lev Rozansky

  • A diagrammatic approach to categorification of quantum groups III

    Mikhail Khovanov;Aaron D. Lauda

  • sl(3) link homology

    Mikhail Khovanov

  • Canonical bases in tensor products and graphical calculus for Uq(2)

    Igor B. Frenkel;Mikhail G. Khovanov

  • Triply-graded link homology and Hochschild homology of Soergel bimodules

    Mikhail Khovanov

  • Patterns in Knot Cohomology, I

    Mikhail Khovanov

  • A categorification of quantum sl(n)

    Mikhail Khovanov;Aaron D. Lauda

  • Link homology and Frobenius extensions

    Mikhail Khovanov

  • A categorification of the Temperley-Lieb algebra and Schur quotients of U(sl(2)) via projective and Zuckerman functors

    Joseph Bernstein;Igor Frenkel;Mikhail Khovanov

  • An invariant of tangle cobordisms

    Mikhail Khovanov

  • A Category for the Adjoint Representation

    Ruth Stella Huerfano;Mikhail Khovanov

  • CATEGORIFICATIONS OF THE COLORED JONES POLYNOMIAL

    Mikhail Khovanov

  • Diagrammatics for Soergel Categories

    Ben Elias;Mikhail Khovanov

  • CROSSINGLESS MATCHINGS AND THE COHOMOLOGY OF (n, n) SPRINGER VARIETIES

    Mikhail Khovanov

  • A categorification of finite-dimensional irreducible representations of quantum $${\mathfrak{sl}_2}$$ and their tensor products

    Igor Frenkel;Mikhail Khovanov;Catharina Stroppel

Frequent Co-Authors

Igor B. Frenkel
Igor B. Frenkel Yale University
Volodymyr Mazorchuk
Volodymyr Mazorchuk Uppsala University
Greg Kuperberg
Greg Kuperberg University of California, Davis
Sergei Gukov
Sergei Gukov California Institute of Technology
Johannes Walcher
Johannes Walcher Heidelberg University
Richard P. Thomas
Richard P. Thomas Imperial College London

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