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Maxim Lvovich Kontsevich (Russian: Максим Львович Концевич) (born 25 August 1964) is a Russian mathematician. He received a Fields Medal in 1998, at the 23rd International Congress of Mathematicians in Berlin. He also received the Henri Poincaré Prize in 1997 and a Crafoord Prize in 2008.


Born into the family of Lev Rafailovich Kontsevich – Soviet orientalist and author of the Kontsevich system. 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 [1]. In 1992 he received his Ph.D. at the University of Bonn under Don Bernard Zagier. His thesis claims to prove a conjecture by Edward Witten that two quantum gravitational models are equivalent. Currently he is a Professor at the Institut des Hautes Études Scientifiques (IHÉS) in Bures-sur-Yvette, France and Distinguished Professor at University of Miami in Coral Gables, Florida, U.S..

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.

See also

* Kontsevich integral
* Homological mirror symmetry
* Motivic integration
* Kontsevich quantization formula
* Ring of periods


* Fields Medal citation at the website of the 2002 International Congress of Mathematicians held in Beijing.
* Taubes, Clifford Henry (1998) "The work of Maxim Kontsevich". In Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998). Doc. Math., Extra Vol. I, 119–126.

External links

* Maxim Kontsevich at the Mathematics Genealogy Project
* AMS Profile of Maxim Kontsevich


Mathematics Encyclopedia

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