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. 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 Etudes 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 Manifolds . He also introduced knot invariants defined by complicated integrals analogous to Feymann integrals. In topological field theory, he introduced the moduli space of stable maps, which may be considered a mathematically rigorous formulation of the Feymann 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.
Free Download his papers
Stability structures, motivic Donaldson-Thomas invariants and cluster transformations,with Yan Soibelman.
Notes on motives in finite characteristic
On Malliavin measures, SLE and CFT, with Yuri Suhov
Automorphisms of the Weyl algebra, with Alexei Belov-Kanel
Affine structures and non-archimedean analytic spaces, with Yan Soibelman
Homological mirror symmetry and torus fibrations, with Yan Soibelman
Deformations of algebras over operads and Deligne's conjecture,with Yan Soibelman
Operads and Motives in Deformation Quantization
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