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

French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with Franc ...

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 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, incl ...

. 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. The prize is sponsored by the Daniel Iagolnitzer Foundat ...

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 the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

in 1998, the Crafoord Prize in 2008, the

Shaw Prize The Shaw Prize is an annual award presented by the Shaw Prize Foundation. Established in 2002 in Hong Kong, it honours "individuals who are currently active in their respective fields and who have recently achieved distinguished and signifi ...

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 capita ...

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, Soviet orientalist and author of the

Kontsevich system The Kontsevich system () is a Cyrillization system for the Korean language and currently the main system of transcribing and transliterating Korean words into the Cyrillic alphabet. The Kontsevich system was created by the Soviet-Russian scholar ...

. After ranking second in the All-Union 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 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 Maxi ...

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

Dr. Doctor is an academic title that originates from the Latin word of the same spelling and meaning. The word is originally an agentive noun of the Latin verb 'to teach'. It has been used as an academic title in Europe since the 13th century, w ...

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 U ...

under

Don Bernard Zagier Don Bernard Zagier (born 29 June 1951) is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max-Planck-Institut für Mathematik, Max Planck Institute for Mathematics in Bonn, Ger ...

. His thesis outlines a proof of a conjecture by Edward Witten 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 Institut des Hautes Études Scientifiques in Bures-sur-Yvette as a permanent member. His work concentrates on geometric aspects of

mathematical physics Mathematical physics refers to 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 t ...

, most notably on

knot theory In the mathematical field of 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 ...

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

deformation quantization Deformation can refer to: * Deformation (engineering), changes in an object's shape or form due to the application of a force or forces. ** Deformation (physics), such changes considered and analyzed as displacements of continuum bodies. * Defor ...

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 In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants. Although TQFTs were invented by physicists, they are also of math ...

, 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 qu ...

. 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. Also in 2012, he was awarded the

. 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