View source for Maxim Kontsevich

{{short description|Russian and French mathematician (born 1964)}}
<!--{{redirect|Kontsevich|the linguist|Lev Kontsevitch}}-->
{{Infobox scientist
| image             = MaximKontsevich.jpg
| image_size        = 170px
| name              = Maxim Kontsevich
| caption           = 
| birth_date        = {{Birth date and age|1964|8|25|df=y}}
| birth_place       = [[Khimki]], [[Russian SFSR]], [[Soviet Union]]
| death_date        = 
| death_place       = 
| citizenship       = [[Russia]]<br/>[[France]]
| nationality       = [[Russians|Russian]]
| ethnicity         = 
| field             = [[Mathematics]], [[Mathematical physics]]
| work_institution  = [[Institut des Hautes Études Scientifiques]]<br />[[University of Miami]]<br />[[University of California, Berkeley]]
| alma_mater        = [[Moscow State University]]<br>[[University of Bonn]]
| doctoral_advisor  = [[Don Bernard Zagier]]
| notable_students  = [[Serguei Barannikov]]
| known_for         = 
| prizes            = [[EMS Prize]] (1992)<br/>[[Otto Hahn Medal]] (1992)<br/>[[Henri Poincaré Prize]] (1997)<br />[[Fields Medal]] (1998)<br />[[Crafoord Prize]] (2008) <br />[[Shaw Prize]] (2012) <br />[[Breakthrough Prize in Fundamental Physics]] (2012)<br />[[Breakthrough Prize in Mathematics]] (2015) <br />National Academy of Sciences (Foreign Associate) (2015)
| religion          = 
| footnotes         = 
}}
'''Maxim Lvovich Kontsevich''' ({{langx|ru|Макси́м Льво́вич Конце́вич}}, {{IPA|ru|mɐkˈsʲim ˈlʲvovʲɪtɕ kɐnˈtsɛvʲɪtɕ|IPA|M_L_Kontsevich.ogg}}; born 25 August 1964)<ref>{{Cite web|url=https://www.britannica.com/biography/Maxim-Kontsevich|title=Maxim Kontsevich {{!}} Russian mathematician|website=Encyclopedia Britannica|language=en|access-date=2020-01-17}}</ref> is a [[Russians|Russian]] and [[French people|French]]<ref>Kontsevich received French citizenship in 1999 and remains a dual citizen of both France and his native Russia.</ref> [[mathematician]] and mathematical physicist. He is a professor at the [[Institut des Hautes Études Scientifiques]] and a distinguished professor at the [[University of Miami]]. He received the [[Henri Poincaré Prize]] in 1997, the [[Fields Medal]] in 1998, the [[Crafoord Prize]] in 2008, the [[Shaw Prize]] and [[Breakthrough Prize in Fundamental Physics]] in 2012, and the [[Breakthrough Prize in Mathematics]] in 2015.<ref>{{cite news|last1=Chang|first1=Kenneth|title=The Multimillion-Dollar Minds of 5 Mathematical Masters|work=The New York Times |url=https://www.nytimes.com/2014/06/23/us/the-multimillion-dollar-minds-of-5-mathematical-masters.html?_r=0|agency=[[The New York Times]]|date=23 June 2014}}</ref>

== Academic career and research ==
He was born into the family of [[Lev Kontsevich]], Soviet orientalist and author of the [[Kontsevich system]]. 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.<ref name="A Very Pleasurable Universe"/> While at the institute he published papers that caught the interest of the [[Max Planck Institute for Mathematics|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]] and other mathematicians and his invitation to the institute was subsequently extended to three years.<ref name="A Very Pleasurable Universe">{{Cite web |first=Robert |last=Sanders |url=https://www.berkeley.edu/news/berkeleyan/1994/1012/math.html |date=October 12, 1994 |title=A Very Pleasurable Universe |website=www.berkeley.edu |access-date=2018-11-23 }}</ref>

The next year he finished the proof and worked on various topics on mathematical physics and in 1992 received his [[Dr. rer. nat.]] at the [[University of Bonn]] under [[Don Bernard Zagier]]. His thesis outlines a proof of a conjecture by [[Edward Witten]] that two [[Quantum gravity|quantum gravitational models]] are equivalent. In 1992, Kontsevich was appointed to a full professorship in mathematics at the [[University of California, Berkeley]], 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]], most notably on [[knot theory]], [[quantization (physics)|quantization]], and [[mirror symmetry (string theory)|mirror symmetry]].  One of his results is a formal [[Kontsevich quantization formula|deformation quantization]] that holds for any [[Poisson manifold]].  He also introduced the [[Kontsevich invariant|Kontsevich integral]], a topological [[Knot invariant|invariant of knots (and links)]] defined by complicated integrals analogous to [[path integral formulation|Feynman integrals]], and generalizing the classical [[Gauss]] [[linking number]]. In [[topological field theory]], he introduced the [[stable map|moduli space of stable maps]], which may be considered a mathematically rigorous formulation of the [[path integral formulation|Feynman integral]] for [[topological string theory]]. He also proved that the [[Dixmier conjecture]] 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."<ref>''Opening ceremony''. [https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1998.1/ICM1998.1.ocr.pdf Proceedings of the International Congress of Mathematicians 1998. Volume I] pp.46–48</ref> In July 2012, he was an inaugural awardee of the [[Breakthrough Prize in Fundamental Physics]], the creation of physicist and internet entrepreneur, [[Yuri Milner]].<ref>[https://breakthroughprize.org/News/15 New annual US$3 million Fundamental Physics Prize recognizes transformative advances in the field] He also served on the Mathematical Sciences jury for the [[Infosys Prize]] in 2011 and 2012. {{webarchive|url=https://web.archive.org/web/20120803211628/https://breakthroughprize.org/News/15 |date=2012-08-03 }}, FPP, accessed 1 August 2012</ref> Also in 2012, he was awarded the [[Shaw Prize]].<ref>{{cite web |title=The 2012 Prize in Mathematical Sciences: Maxim Kontsevich |url=https://www.shawprize.org/laureates/mathematical-sciences/2012 |access-date=29 June 2020}}</ref> In 2015, he was awarded [[Breakthrough Prize in Mathematics]].

== Notes ==
<references />

== References ==
* [https://web.archive.org/web/20061001142812/http://www.icm2002.org.cn/general/prize/medal/1998.htm#Maxim Fields Medal citation] at the website of the [https://web.archive.org/web/20090930110041/http://www.icm2002.org.cn/ 2002 International Congress of Mathematicians] held in [[Beijing]].
* 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 ==
* {{MacTutor Biography|id=Kontsevich}}
* {{MathGenealogy |id=26861}}
* [https://www.ams.org/featurecolumn/archive/kontsevich.html AMS Profile of Maxim Kontsevich]
* [https://www.ihes.fr/~maxim/ Official Homepage of Maxim Kontsevich]
* [https://av.tib.eu/search?f=creator%3Bhttp://d-nb.info/gnd/113375522,creator%3Bhttp://av.tib.eu/resource/Konsevitch__Maxim Videos of Maxim Kontsevich] in the AV-Portal of the [[German National Library of Science and Technology]]

{{Fields medalists}}
{{Shaw Prize laureates}}
{{Breakthrough Prize laureates}}

{{Authority control}}

{{DEFAULTSORT:Kontsevich, Maxim}}
[[Category:1964 births]]
[[Category:Living people]]
[[Category:20th-century Russian mathematicians]]
[[Category:21st-century Russian mathematicians]]
[[Category:Moscow State University alumni]]
[[Category:Fields Medalists]]
[[Category:University of California, Berkeley faculty]]
[[Category:Rutgers University faculty]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Foreign associates of the National Academy of Sciences]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Topologists]]
[[Category:Differential geometers]]
[[Category:Algebraic geometers]]
[[Category:University of Bonn alumni]]
[[Category:Russian scientists]]