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.
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