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Maxim Lvovich Kontsevich (, ; born 25 August 1964) is a Russians and French peopleKontsevich received French citizenship in 1999 and remains a dual citizen of both France and his native Russia. mathematician and mathematical physicist. 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, the Crafoord Prize in 2008, the Shaw Prize and Breakthrough Prize in Fundamental Physics in 2012, and the Breakthrough Prize in Mathematics in 2015.
The next year he finished the proof and worked on various topics on mathematical physics and in 1992 received his Dr. rer. nat. at the University of Bonn under Don Bernard Zagier. His thesis outlines a proof of a conjecture by Edward Witten that two Quantum gravity are equivalent. In 1992, Kontsevich was appointed to a full professorship in mathematics at the University of California, Berkeley, before moving in 1995 to France, where he joined the Institut des Hautes Études Scientifiques in Bures-sur-Yvette as a permanent member.
His work concentrates on geometric aspects of mathematical physics, most notably on knot theory, quantization, and mirror symmetry. One of his results is a formal deformation quantization that holds for any Poisson manifold. He also introduced the Kontsevich integral, a topological Knot invariant defined by complicated integrals analogous to Feynman integrals, and generalizing the classical Gauss linking number. In topological field theory, he introduced the stable map, which may be considered a mathematically rigorous formulation of the Feynman integral for topological string theory. He also proved that the Dixmier conjecture is equivalent to the Jacobian conjecture.
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