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

Russian Russian(s) may refer to: *Russians (), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *A citizen of Russia *Russian language, the most widely spoken of the Slavic languages *''The Russians'', a b ...

and

French French may refer to: * Something of, from, or related to France ** French language, which originated in France ** French people, a nation and ethnic group ** French cuisine, cooking traditions and practices Arts and media * The French (band), ...

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 The Shaw Prize is a set of three annual awards presented by the Shaw Prize Foundation in the fields of astronomy, medicine and life sciences, and mathematical sciences. Established in 2002 in Hong Kong, by Hong Kong entertainment mogul and p ...

and

Breakthrough Prize in Fundamental Physics 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 2015.

Academic career and research

He was born into the family of

Lev Kontsevich Lev Rafailovich Kontsevich (, , born 3 September 1930) is a Soviet-Russian orientalist and Candidate of Sciences, who created the Kontsevich system, the one of cyrillization system for the Korean language and currently the main system of trans ...

, Soviet orientalist and author of the

Kontsevich system The Cyrillization of Korean is the transcribing and transliterating the Korean language into the Cyrillic alphabet. The main cyrillization system in use is the Kontsevich system (). The Kontsevich system was created by the Soviet-Russian schola ...

. 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 The Mathematische Arbeitstagung taking place annually in Bonn since 1957, and founded by Friedrich Hirzebruch, was an international meeting of mathematicians intended to act in clearing-house fashion, by disseminating current research ideas; and, ...

, 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 Max ...

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. for, la, Doctor rerum naturalium, Doctor of Natural Sciences, paren=left, ), abbreviated Dr. rer. nat., is a doctoral academic degree awarded by universities in some European countries (e.g. Germany, Austria and Czech Republic) to graduates in phy ...

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

Bures-sur-Yvette Bures-sur-Yvette (, "Bures-on- Yvette") is a commune in the Essonne department in the Île-de-France region in Northern France. It is a southern Parisian outer suburb in the Vallée de Chevreuse, with a population of 9,254 as of 2021. Geograp ...

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 In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a Reflection (mathematics), reflection. That is, a figure which does not change upon undergoing a reflection has reflecti ...

. 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 In differential geometry, a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in turn generalises the phase space from Hami ...

. 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 (; ; ; 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 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 stationary action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or ...

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 con ...

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

, the creation of physicist and internet entrepreneur,

Yuri Milner Yuri Borisovich (Bentsionovich) Milner (, ; born 11 November 1961) is a Soviet-born Israeli entrepreneur, investor, physicist and scientist. He is a co-founder and former chairperson of internet company Mail.Ru Group (later VK), and a founder ...

. Also in 2012, he was awarded the

. In 2015, he was awarded

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 The German National Library of Science and Technology (), abbreviated TIB, is the national library of the Federal Republic of Germany for all fields of engineering, technology, and the natural sciences. It is jointly funded by the Federal Mini ...

{{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