ⓘ Maxim Kontsevich
Maxim Lvovich Kontsevich ; born 25 August 1964) is a Russian and French mathematician. He is a professor at the Institut des Hautes Etudes Scientifiques and a distinguished professor at the University of Miami. He received the Henri Poincare Prize in 1997, the Fields Medal in 1998, the Crafoord Prize in 2008, the Shaw Prize and Fundamental Physics Prize in 2012, and the Breakthrough Prize in Mathematics in 2014.
1. Biography
He was born into the family of Lev Rafailovich Kontsevich, Soviet orientalist and author of the Kontsevich system. After ranking second in the AllUnion Mathematics Olympiads, he attended Moscow State University but left without a degree in 1985 to become a researcher at the Institute for Information Transmission Problems in Moscow. While at the institute he published papers that caught the interest of the Max Planck Institute in Bonn and was invited for three months. Just before the end of his time there, he attended a fiveday international meeting, the Arbeitstagung, where he sketched a proof of the Witten conjecture to the amazement of Michael Atiyah and other mathematicians and his invitation to the institute was subsequently extended to three years. The next year he finished the proof and worked on various topics on mathematical physics and in 1992 received his Ph.D. at the University of Bonn under Don Bernard Zagier. His thesis outlines a proof of 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. One of his results is a formal deformation quantization that holds for any Poisson manifold. He also introduced the Kontsevich integral, a topological invariant of knots and links defined by complicated integrals analogous to Feynman integrals, and generalizing the classical Gauss linking number. 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.
2. Honors and awards
In 1998, he won the Fields Medal for his "contributions to four problems of Geometry". In July 2012, he was an inaugural awardee of the Fundamental Physics Prize, the creation of physicist and internet entrepreneur, Yuri Milner. In 2014, he was awarded Breakthrough Prize in Mathematics.
 Lie algebra Notable results of Willwacher include the proof of Maxim Kontsevich s cyclic formality conjecture and the proof that the Grothendieck Teichmuller
 noncommutative geometry, Ginzburg defined, following earlier ideas of Maxim Kontsevich the notion of Calabi Yau algebra. An important role in the theory
 Ramon Jimenez Nobel Prize  winning author Neil F. Johnson Physics Maxim Kontsevich Mathematics Behram Kursunoğlu Physics Abraham Lavender Sociology
 Barannikov Morse complexes, Barannikov modules, Barannikov Kontsevich construction, and Barannikov Kontsevich theorem. Serguei Barannikov at the Mathematics Genealogy
 103 1 547. Bibcode: 1991InMat.103..547R. doi: 10.1007 BF01239527. Kontsevich Maxim 1993 Vassiliev s knot invariants Adv. Soviet Math. 16: 137.
 Madhav Nori. In 2003, together with Patrick Brosnan, Belkale disproved Maxim Kontsevich s Spanning  Tree Conjecture first published in 1997 Let G be a finite
 Fields Medalist Maxim Kontsevich to result from integration, using the Kontsevich integral, of certain algebraic structures Kontsevich 1993, Bar  Natan
 Mathematicians in Berlin, Germany he received the Fields Medal together with Maxim Kontsevich William Timothy Gowers and Curtis T. McMullen. The award cited him
 Oxford Univ Press Enumeration Of Rational Curves Via Torus Actions, Maxim Kontsevich 1995 Non  commutative Calculus and Discrete Physics, Louis H. Kauffman
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