Maxim Lwowitsch Konzewitsch

Maxim Lwowitsch Konzewitsch ( Russian Максим Львович Концевич , in the literature mostly cited in the English form "Maxim Kontsevich"; born  August 25, 1964 in Chimki ) is a Franco- Russian mathematician .

Maxim Kontsevich

Life

After he finished second in the Soviet Mathematics Olympiad as a student, he studied mathematics at Lomonosov University in Moscow . From 1985 he was a research mathematician at the "Institute for Problems of Information Transmission" (IITP RAS) in Moscow. In 1992 he did his doctorate at the University of Bonn under Don Bernard Zagier , where he proved a conjecture by Edward Witten about the equivalence of two models of quantum gravity . He is currently Professor at the Institut des Hautes Études Scientifiques ( IHÉS ) in Bures-sur-Yvette , France , and visiting professor at Rutgers University in New Brunswick, New Jersey , USA .

Other important work also takes place in the field of mathematical physics, often following ideas from the field of string theory . He found a construction for knot invariants from Feynman integrals of topological quantum field theories. All Vassiliev knot invariants can be constructed in this way. In algebraic geometry he found methods for counting rational algebraic curves on certain varieties . He partly worked with Yuri Manin , with whom he formulated a conjecture about “mirror symmetry” of three-dimensional Calabi-Yau manifolds (see Floer homology ). Another important result is his quantization of general Poisson manifolds and further contributions to non-commutative geometry .

He has French and Russian citizenship.

Prices and memberships

• 1992 EMS Prize
• 1992 Otto Hahn Medal
• 1992 Prix Européen de la Ville de Paris
• 1998 Fields Medal
• 2008 Crafoord Prize
• 2012 Shaw Prize (for work on deformation quantization, motivic integration and mirror symmetry).
• 2012 Fundamental Physics Prize
• 2014 Breakthrough Prize in Mathematics together with four other mathematicians. The laudation highlighted his profound influence in a large number of mathematical fields, including algebraic geometry, deformation theory, symplectic geometry, homological algebra and dynamic systems .

In 1998 he received the Fields Medal at the 23rd International Congress of Mathematicians in Berlin alongside Richard Borcherds , William Timothy Gowers and Curtis T. McMullen . In 1997 he received the Henri Poincaré Prize . In 1994 he gave a plenary lecture at the ICM in Zurich (Homological algebra of mirror symmetry). In 1992 he was invited speaker at the European Congress of Mathematicians in Paris ( Feynman diagrams and low dimensional topology ).

He is a member of the Institut de France and the Academia Europaea . He has been a member of the Académie des Sciences since 2002 and of the National Academy of Sciences since 2015 .

Fonts (selection)

Except for the works cited in the footnotes.

• Manin, Kontsevich: Gromov-Witten classes, quantum cohomology and enumerative geometry , Comm. Math. Phys., Volume 164, 1994, pp. 525-562, arxiv : hep-th / 9402147 ;
• Kontsevich: Enumeration of rational curves via torus actions . 1994, arxiv : hep-th / 9405035
• with Don Zagier : Periods , in Engquist a. a. Mathematics Unlimited , Springer 2001, pdf
• Kontsevich: Deformation quantization of Poisson manifolds , Lett. Math. Phys., Volume 66, 2003, pp. 157-216, arxiv : q-alg / 9709040

literature

• Clifford Taubes The work of Maxim Kontsevich , ICM Berlin 1998, online here: math.uni-bielefeld.de

Web links

Commons : Maxim Kontsevich  - collection of images, videos and audio files

• John J. O'Connor, Edmund F. Robertson :  Maxim Lwowitsch Konzewitsch. In: MacTutor History of Mathematics archive .
• Fields Medal Award by the AMS 1998 (English)
• Fields Medal Winner Biographies. 1998 (english)
• Videos by Maxim Konzewitsch (English) in the AV portal of the Technical Information Library

Individual evidence

1. ↑ Intersection theory on the moduli space of curves and the Matrix Airy Function , Communications in Mathematical Physics Vol. 147, 1992, pp. 1-23. Witten speculated more precisely that a generating function, with the intersection numbers of varieties in the module space (classification space) of curves (of gender g with n marked points) as coefficients, suffices an exactly integrable ( Korteweg-de-Vries ) differential equation.
2. ↑ Feynman diagrams and low dimensional topology , 1st European Congress of Mathematics, Paris 1992, Birkhäuser Verlag 1994, vol. 2, p. 97
3. ↑ Enumeration of rational curves via Torus Actions , in Dijkgraaf et al. a. Progress in Mathematics Vol. 129, 1995, pp. 120-139
4. ↑ Deformation quantization of Poisson manifolds , Letters Math. Physics Vol. 66, 2003, pp. 157-216
5. ^ Entry by Kontsevich at the Academie des Sciences, accessed October 28, 2012 ( Memento of the original from December 5, 2014 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
6. ↑ Breakthrough Prize 2014 ( Memento of the original from June 24, 2014 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.