Maxim Kontsevich
Encyclopedia
Maxim Lvovich Kontsevich is a Russian
mathematician
. He is a professor at the Institut des Hautes Études Scientifiques
and a distinguished professor at the University of Miami
. He received the Henri Poincaré Prize in 1997, the Fields Medal
in 1998, and the Crafoord Prize
in 2008.
. After ranking second in the All-Union Mathematics Olympiads, he attended Moscow State University
but left without a degree in 1985 to become a researcher at the Institute for Problems of Information Transmission in Moscow http://www.berkeley.edu/news/berkeleyan/1994/1012/math.html. In 1992 he received his Ph.D.
at the University of Bonn
under Don Bernard Zagier. His thesis proves a conjecture by Edward Witten
that two quantum gravitational models are equivalent.
His work concentrates on geometric aspects of mathematical physics
, most notably on knot theory
, quantization
, and mirror symmetry
. His most famous result is a formal deformation quantization
that holds for any Poisson manifold
. He also introduced knot invariants defined by complicated integrals analogous to Feynman integrals
. In topological field theory, he introduced the moduli space of stable maps
, which may be considered a mathematically rigorous formulation of the Feynman integral
for topological string theory. These results are a part of his "contributions to four problems of geometry" for which he was awarded the Fields Medal
in 1998.
Russians
The Russian people are an East Slavic ethnic group native to Russia, speaking the Russian language and primarily living in Russia and neighboring countries....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is a professor at the Institut des Hautes Études Scientifiques
Institut des Hautes Études Scientifiques
The Institut des Hautes Études Scientifiques is a French institute supporting advanced research in mathematics and theoretical physics...
and a distinguished professor at the University of Miami
University of Miami
The University of Miami is a private, non-sectarian university founded in 1925 with its main campus in Coral Gables, Florida, a medical campus in Miami city proper at Civic Center, and an oceanographic research facility on Virginia Key., the university currently enrolls 15,629 students in 12...
. He received the Henri Poincaré Prize in 1997, the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
in 1998, and the Crafoord Prize
Crafoord Prize
The Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord...
in 2008.
Biography
Born into the family of Lev Rafailovich Kontsevich – Soviet orientalist and author of the Kontsevich systemKontsevich system
The Kontsevich system for the Cyrillization of the Korean language was created by the Russian scholar Lev Kontsevitch on the basis of the earlier system designed by Aleksandr Kholodovich...
. After ranking second in the All-Union Mathematics Olympiads, he attended Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
but left without a degree in 1985 to become a researcher at the Institute for Problems of Information Transmission in Moscow http://www.berkeley.edu/news/berkeleyan/1994/1012/math.html. In 1992 he received his Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
at the University of Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
under Don Bernard Zagier. His thesis proves a conjecture by Edward Witten
Edward Witten
Edward Witten is an American theoretical physicist with a focus on mathematical physics who is currently a professor of Mathematical Physics at the Institute for Advanced Study....
that two quantum gravitational models are equivalent.
His work concentrates on geometric aspects of mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
, most notably on 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...
, quantization
Quantization (physics)
In physics, quantization is the process of explaining a classical understanding of physical phenomena in terms of a newer understanding known as "quantum mechanics". It is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the...
, and mirror symmetry
Mirror symmetry
In physics and mathematics, mirror symmetry is a relation that can exist between two Calabi-Yau manifolds. It happens, usually for two such six-dimensional manifolds, that the shapes may look very different geometrically, but nevertheless they are equivalent if they are employed as hidden...
. His most famous result is a formal deformation quantization
Quantization (physics)
In physics, quantization is the process of explaining a classical understanding of physical phenomena in terms of a newer understanding known as "quantum mechanics". It is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the...
that holds for any Poisson manifold
Poisson manifold
In mathematics, a Poisson manifold is a differentiable manifold M such that the algebra C^\infty\, of smooth functions over M is equipped with a bilinear map called the Poisson bracket, turning it into a Poisson algebra...
. He also introduced knot invariants defined by complicated integrals analogous to Feynman integrals
Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
. In topological field theory, he introduced the moduli space of stable maps
Stable map
In mathematics, specifically in symplectic topology and algebraic geometry, one can construct the moduli space of stable maps, satisfying specified conditions, from Riemann surfaces into a given symplectic manifold. This moduli space is the essence of the Gromov–Witten invariants, which find...
, which may be considered a mathematically rigorous formulation of the Feynman integral
Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
for topological string theory. These results are a part of his "contributions to four problems of geometry" for which he was awarded the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
in 1998.
See also
- Kontsevich integralKontsevich invariantIn the mathematical theory of knots, the Kontsevich invariant, also known as the Kontsevich integral, of an oriented framed link is the universal finite type invariant in the sense that any coefficient of the Kontsevich invariant is a finite type invariant, and any finite type invariant can be...
- Homological mirror symmetryHomological mirror symmetryHomological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory.-History:...
- Motivic integrationMotivic integrationMotivic integration is a branch of algebraic geometry which was invented by Maxim Kontsevich in 1995 and was developed by Jan Denef and François Loeser. Since its introduction it has proved to be quite useful in various branches of algebraic geometry, most notably birational geometry and...
- Kontsevich quantization formulaKontsevich quantization formulaIn mathematics, the Kontsevich quantization formula describes how to construct an generalized ∗-product operator algebra from a given Poisson manifold. This operator algebra amounts to the deformation quantization of the Poisson algebra...
- Ring of periods