Maxim Lvovich Kontsevich (russian: Макси́м Льво́вич Конце́вич, ; born 25 August 1964) is a

Russian Russian(s) refers to anything related to Russia, including: *Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *Rossiyane (), Russian language term for all citizens and peo ...

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, structure, space, models, and change. History On ...

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. It is located in Bures-sur-Yvette, jus ...

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 research university in Coral Gables, Florida. , the university enrolled 19,096 students in 12 colleges and schools across nearly 350 academic majors and programs, i ...

. He received the Henri Poincaré Prize in 1997, the Fields Medal 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. The Prize is awarded in partnership between the Royal Swedish Academy of Sciences and the Crafoord Foun ...

in 2008, the Shaw Prize and

Fundamental Physics Prize The Breakthrough Prize in Fundamental Physics is one of the Breakthrough Prizes, awarded by the Breakthrough Prize Board. Initially named Fundamental Physics Prize, it was founded in July 2012 by Russia-born Israeli entrepreneur, venture capit ...

in 2012, and the

Breakthrough Prize in Mathematics The Breakthrough Prize in Mathematics is an annual award of the Breakthrough Prize series announced in 2013. It is funded by Yuri Milner and Mark Zuckerberg and others. The annual award comes with a cash gift of $3 million. The Breakthrough Prize ...

in 2014.

Academic career and research

He was born into the family of

Lev Kontsevich Lev Rafailovich Kontsevich ( rus, Лев Рафаилович Концевич, , born 3 September 1930) is a Soviet- Russian orientalist and Candidate of Sciences, who created the Kontsevich system, the cyrillization system for the Korean langua ...

, Soviet orientalist and author of the Kontsevich system. After ranking second in the All-Union Mathematics Olympiads, he attended

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

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 In algebraic geometry, the Witten conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by Edward Witten in the paper , and generalized in . Witten's original conjecture was proved by Ma ...

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 th ...

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. at the

University of Bonn The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine ...

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

Edward Witten Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, q ...

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 land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

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

Bures-sur-Yvette Bures-sur-Yvette (, literally ''Bures on Yvette'') is a commune in the Essonne department in Île-de-France in northern France. Geography Bures-sur-Yvette is located in the Vallée de Chevreuse on the river Yvette, along which the RER line&nb ...

as a permanent member. His work concentrates on geometric aspects of

mathematical physics Mathematical physics refers to the development of 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 developme ...

, most notably on knot theory, quantization, and

mirror symmetry In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D ther ...

. One of his results is a formal deformation quantization that holds for any

Poisson manifold In differential geometry, a Poisson structure on a smooth manifold M is a Lie bracket \ (called a Poisson bracket in this special case) on the algebra (M) of smooth functions on M , subject to the Leibniz rule : \ = \h + g \ . Equivalent ...

. He also introduced the

Kontsevich integral In the mathematical theory of knots, the Kontsevich invariant, also known as the Kontsevich integral of an oriented framed link, is a universal Vassiliev invariant in the sense that any coefficient of the Kontsevich invariant is of a finite type ...

, a topological invariant of knots (and links) defined by complicated integrals analogous to Feynman integrals, and generalizing the classical

Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

linking number In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the linking number represents the number of times that each curve winds around the other. In E ...

. In topological field theory, he introduced the moduli space of stable maps, which may be considered a mathematically rigorous formulation of the

Feynman integral The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional i ...

for

topological string theory In theoretical physics, topological string theory is a version of string theory. Topological string theory appeared in papers by theoretical physicists, such as Edward Witten and Cumrun Vafa, by analogy with Witten's earlier idea of topological ...

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

Jacobian conjecture In mathematics, the Jacobian conjecture is a famous unsolved problem concerning polynomials in several variables. It states that if a polynomial function from an ''n''-dimensional space to itself has Jacobian determinant which is a non-zero co ...

Honors and awards

In 1998, he won the Fields Medal "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

, the creation of physicist and internet entrepreneur,

Yuri Milner Yuri Borisovich (Bentsionovich) Milner (russian: Юрий Борисович (Бенционович) Мильнер; born 11 November 1961) is a Soviet-born Israeli entrepreneur, venture capitalist and physicist. He is a cofounder and former c ...

. Also in 2012, he was awarded the Shaw Prize. In 2014, he was awarded

Notes

References

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

Beijing } Beijing ( ; ; ), alternatively romanized as Peking ( ), is the capital of the People's Republic of China. It is the center of power and development of the country. Beijing is the world's most populous national capital city, with over 21 ...

. * 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 The German National Library of Science and Technology (german: Technische Informationsbibliothek), abbreviated TIB, is the national library of the Federal Republic of Germany for all fields of engineering, technology, and the natural sciences. I ...

{{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