D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 31 Citations 8,498 73 World Ranking 2071 National Ranking 849

Overview

What is he best known for?

The fields of study he is best known for:

  • Pure mathematics
  • Algebra
  • Vector space

His primary areas of investigation include Pure mathematics, Algebra, Categorification, Homology and Diagrammatic reasoning. His study in Khovanov homology, Cohomology, Invariant and Braid group falls within the category of Pure mathematics. The Algebra study combines topics in areas such as Calculus and Calculus.

His Categorification research includes elements of 2-category and Algebra over a field, Root datum. In his study, which falls under the umbrella issue of Homology, Representation theory, Linear algebra and Hypersurface is strongly linked to Euler characteristic. Within one scientific family, Mikhail Khovanov focuses on topics pertaining to Discrete mathematics under Cellular homology, and may sometimes address concerns connected to Relative homology.

His most cited work include:

  • A categorification of the Jones polynomial (826 citations)
  • Matrix factorizations and link homology (540 citations)
  • A diagrammatic approach to categorification of quantum groups II (440 citations)

What are the main themes of his work throughout his whole career to date?

His primary scientific interests are in Pure mathematics, Categorification, Algebra, Homology and Functor. His Pure mathematics study frequently links to other fields, such as Discrete mathematics. His work carried out in the field of Categorification brings together such families of science as Hecke algebra, Symmetric group and Lie algebra.

His Algebra research integrates issues from Algebra over a field and Calculus. His Functor study combines topics from a wide range of disciplines, such as Vector space, Morphism and Grothendieck group. Mikhail Khovanov interconnects Bracket polynomial, Derived category, Combinatorics and Quantum algebra in the investigation of issues within Cohomology.

He most often published in these fields:

  • Pure mathematics (68.60%)
  • Categorification (38.02%)
  • Algebra (30.58%)

What were the highlights of his more recent work (between 2017-2021)?

  • Pure mathematics (68.60%)
  • Homology (18.18%)
  • Equivariant map (3.31%)

In recent papers he was focusing on the following fields of study:

His main research concerns Pure mathematics, Homology, Equivariant map, Functor and Tensor. His study in Cobordism, Categorification, Morphism, Vector space and Special functions falls under the purview of Pure mathematics. His Categorification studies intersect with other subjects such as Diagrammatic reasoning and Reciprocity.

Mikhail Khovanov has researched Homology in several fields, including Formal group and Graph. His study focuses on the intersection of Tensor and fields such as Series with connections in the field of Algebra over a field. His research integrates issues of Homotopy category and Algebra in his study of Algebra over a field.

Between 2017 and 2021, his most popular works were:

  • Link homology and Frobenius extensions II (16 citations)
  • Foam evaluation and Kronheimer--Mrowka theories (8 citations)
  • A deformation of Robert-Wagner foam evaluation and link homology (6 citations)

In his most recent research, the most cited papers focused on:

  • Pure mathematics
  • Algebra
  • Vector space

Mikhail Khovanov mainly focuses on Pure mathematics, Homology, Equivariant map, Categorical variable and Algebra over a field. As part of his studies on Homology, he often connects relevant areas like Formal group. His Categorical variable research incorporates a variety of disciplines, including Braid group, Duality, Action, Action and Algebra.

His research on Algebra over a field often connects related topics like Homotopy category.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

A categorification of the Jones polynomial

Mikhail Khovanov.
Duke Mathematical Journal (2000)

1230 Citations

Matrix factorizations and link homology

Mikhail Khovanov;Lev Rozansky.
Fundamenta Mathematicae (2008)

675 Citations

A diagrammatic approach to categorification of quantum groups II

Mikhail Khovanov;Aaron D. Lauda.
Representation Theory of The American Mathematical Society (2009)

570 Citations

Quivers, Floer cohomology, and braid group actions

Mikhail Khovanov;Paul Seidel.
Journal of the American Mathematical Society (2001)

425 Citations

A diagrammatic approach to categorification of quantum groups III

Mikhail Khovanov;Aaron D. Lauda.
arXiv: Quantum Algebra (2008)

413 Citations

A functor-valued invariant of tangles

Mikhail Khovanov.
Algebraic & Geometric Topology (2002)

402 Citations

Matrix factorizations and link homology II

Mikhail Khovanov;Lev Rozansky.
Geometry & Topology (2008)

389 Citations

sl(3) link homology

Mikhail Khovanov.
Algebraic & Geometric Topology (2004)

284 Citations

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

Igor B. Frenkel;Mikhail G. Khovanov.
Duke Mathematical Journal (1997)

284 Citations

Triply-graded link homology and Hochschild homology of Soergel bimodules

Mikhail Khovanov.
International Journal of Mathematics (2007)

247 Citations

Best Scientists Citing Mikhail Khovanov

Masaki Kashiwara

Masaki Kashiwara

University of Tokyo

Publications: 44

Jonathan Brundan

Jonathan Brundan

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Volodymyr Mazorchuk

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Alexander Kleshchev

Alexander Kleshchev

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Peter Ozsvath

Peter Ozsvath

Princeton University

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Sergei Gukov

Sergei Gukov

California Institute of Technology

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Louis H. Kauffman

Louis H. Kauffman

University of Illinois at Chicago

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Alexei Morozov

Alexei Morozov

Institute on Taxation and Economic Policy

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Weiqiang Wang

Weiqiang Wang

University of Virginia

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Zoltan Szabo

Zoltan Szabo

Princeton University

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Stavros Garoufalidis

Stavros Garoufalidis

Southern University of Science and Technology

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Igor B. Frenkel

Igor B. Frenkel

Yale University

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Richard P. Thomas

Richard P. Thomas

Imperial College London

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Matilde Marcolli

Matilde Marcolli

California Institute of Technology

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Thomas Lam

Thomas Lam

University of Michigan–Ann Arbor

Publications: 6

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking d-index is inferred from publications deemed to belong to the considered discipline.

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