Mikhail Khovanov is a professor of mathematics at Columbia University

Columbia University

Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...

. He earned a PhD in mathematics from Yale University

Yale University

Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...

 in 1997, where he studied under Igor Frenkel

Igor Frenkel

Igor Borisovich Frenkel is a mathematician at Yale University working in representation theory and mathematical physics.-Biography:...

. His interests include knot theory

Knot theory

In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...

 and algebraic topology

Algebraic topology

Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...

. He is most well known for the Khovanov homology

Khovanov homology

In mathematics, Khovanov homology is an invariant of oriented knots and links that arises as the homology of a chain complex. It may be regarded as a categorification of the Jones polynomial....

 for links

Link (knot theory)

In mathematics, a link is a collection of knots which do not intersect, but which may be linked together. A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory...

, introduced in his seminal paper "A categorification of the Jones polynomial", which he published while at UC Davis. This was one of the first examples of categorification

Categorification

In mathematics, categorification refers to the process of replacing set-theoretic theorems by category-theoretic analogues. Categorification, when done successfully, replaces sets by categories, functions with functors, and equations by natural isomorphisms of functors satisfying additional...

and spawned a new direction of research in knot theory.

External links

• Khovanov's faculty page at Columbia.
• List of Khovanov's publications.