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, mathematical structure, structure, space, Mathematica ...
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, ...
. 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 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 Fo ...
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 in 2012, and the
Breakthrough Prize in Mathematics 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
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 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 t ...
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
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
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, ...
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,
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
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 \ .
Equivalen ...
. 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 (; 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
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 for
topological string theory. He also proved that the
Dixmier conjecture
In algebra the Dixmier conjecture, asked by Jacques Dixmier in 1968, is the conjecture that any endomorphism of a Weyl algebra is an automorphism.
Tsuchimoto in 2005, and independently Belov-Kanel and Kontsevich in 2007, showed that the Dixm ...
is equivalent to the
Jacobian conjecture.
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
Fundamental Physics Prize, the creation of physicist and internet entrepreneur,
Yuri Milner. Also in 2012, he was awarded 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 ...
.
In 2014, he was awarded
Breakthrough Prize in Mathematics.
Notes
References
Fields Medal citationat the website of th
2002 International Congress of Mathematiciansheld 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 KontsevichOfficial Homepage of Maxim KontsevichVideos of Maxim Kontsevichin 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