Mikhail Khovanov (russian: Михаил Гелиевич Хованов; born 1972) is a

Russia Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-eigh ...

n- American professor of mathematics at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manha ...

who works on

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

knot theory In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot ...

, and

algebraic topology Algebraic topology is a branch of mathematics that 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 classif ...

. He is known for introducing

Khovanov homology In mathematics, Khovanov homology is an oriented link invariant that arises as the cohomology of a cochain complex. It may be regarded as a categorification of the Jones polynomial. It was developed in the late 1990s by Mikhail Khovanov, then at ...

for links, which was one of the first examples of

categorification In mathematics, categorification is the process of replacing set-theoretic theorems with category-theoretic analogues. Categorification, when done successfully, replaces sets with categories, functions with functors, and equations with natu ...

Education and career

Khovanov graduated from Moscow State School 57 mathematical class in 1988. He earned a PhD in mathematics from

Yale University Yale University is a Private university, private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the List of Colonial Colleges, third-oldest institution of higher education in the United Sta ...

in 1997, where he studied under Igor Frenkel. Khovanov was a faculty member at

UC Davis The University of California, Davis (UC Davis, UCD, or Davis) is a Public university, public Land-grant university, land-grant research university near Davis, California. Named a Public Ivy, it is the northernmost of the ten campuses of the Uni ...

before moving to Columbia University."Mathematics", UC Davis Wiki
4 April 2007.

"Mikhail Khovanov was in the department when he developed the famous homology theory that bears his name."

He is a half-brother of Tanya Khovanova.

References

External links

Khovanov's faculty page
at Columbia.
List of Khovanov's publications
1972 births Living people 20th-century American mathematicians 21st-century American mathematicians Topologists Columbia University faculty Yale University alumni {{US-mathematician-stub