Maxim Lvovich Kontsevich (, ; born 25 August 1964) is a Russian and French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and mathematical physicist. He is a professor at the

Institut des Hautes Études Scientifiques The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics (also with a small theoretical biology g ...

and a distinguished professor at the

University of Miami The University of Miami (UM, UMiami, Miami, U of M, and The U) is a private university, private research university in Coral Gables, Florida, United States. , the university enrolled 19,852 students in two colleges and ten schools across over ...

. He received the

Henri Poincaré Prize The Henri Poincaré Prize is awarded every three years since 1997 for exceptional achievements in mathematical physics and foundational contributions leading to new developments in the field. It is named after the French mathematician Henri Poincar ...

in 1997, the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...

in 1998, the

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 following a donation to the Royal Swedish Academy of Sciences. It is awarded jointly by the Acade ...

in 2008, the Shaw Prize and Breakthrough Prize in Fundamental Physics in 2012, and the Breakthrough Prize in Mathematics in 2015.

Academic career and research

He was born into the family of Lev Kontsevich, Soviet orientalist and author of the Kontsevich system. After ranking second in the All-Union Mathematics Olympiads, he attended

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

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 five-day international meeting, the Arbeitstagung, where he sketched a proof of the Witten conjecture to the amazement of

Michael Atiyah Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the ...

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 Dr. rer. nat. at the

University of Bonn The University of Bonn, officially the Rhenish Friedrich Wilhelm University of Bonn (), is a public research university in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the () on 18 October 1818 by Frederick Willi ...

under Don Bernard Zagier. His thesis outlines a proof of a conjecture by

Edward Witten Edward Witten (born August 26, 1951) is an American theoretical physics, theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics. He is a professor emeritus in the sc ...

that two quantum gravitational models are equivalent. In 1992, Kontsevich was appointed to a full professorship in mathematics at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, before moving in 1995 to France, where he joined the

in Bures-sur-Yvette as a permanent member. His work concentrates on geometric aspects of

mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

, most notably on

knot theory In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be und ...

, quantization, and mirror symmetry. One of his results is a formal

deformation quantization In mathematics and physics, deformation quantization roughly amounts to finding a (quantum) algebra whose classical limit is a given (classical) algebra such as a Lie algebra or a Poisson algebra. In physics Intuitively, a deformation of a math ...

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 Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

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. He also proved that the Dixmier conjecture is equivalent to the Jacobian conjecture.

Honors and awards

In 1998, he won the

"for his contributions to algebraic geometry, topology, and mathematical physics, including the proof of Witten's conjecture of intersection numbers in moduli spaces of stable curves, construction of the universal Vassiliev invariant of knots, and formal quantization of Poisson manifolds." In July 2012, he was an inaugural awardee of the Breakthrough Prize in Fundamental Physics, the creation of physicist and internet entrepreneur, Yuri Milner. Also in 2012, he was awarded the Shaw Prize. In 2015, he was awarded Breakthrough Prize in Mathematics.

Notes

References

Fields Medal citation
at the website of th
2002 International Congress of Mathematicians
held in

Beijing Beijing, Chinese postal romanization, previously romanized as Peking, is the capital city of China. With more than 22 million residents, it is the world's List of national capitals by population, most populous national capital city as well as ...

. * 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

* *
AMS Profile of Maxim Kontsevich

Official Homepage of Maxim Kontsevich

Videos of Maxim Kontsevich
in the AV-Portal of the German National Library of Science and Technology {{DEFAULTSORT:Kontsevich, Maxim 1964 births Living people 20th-century Russian mathematicians 21st-century Russian mathematicians Moscow State University alumni Fields Medalists University of California, Berkeley faculty Rutgers University faculty Members of the French Academy of Sciences Foreign associates of the National Academy of Sciences Institute for Advanced Study visiting scholars Topologists Differential geometers Algebraic geometers University of Bonn alumni Russian scientists