# Igor Frenkel

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{{Short description|Russian-American mathematician}}
{{Infobox scientist
| name              = Igor Frenkel
| image             =
| caption           = Igor Frenkel
| birth_date        = {{Birth date and age|1952|04|22|df=y}}
| birth_place       = [Leningrad](/source/St._Petersburgh), [Soviet Union](/source/Soviet_Union) (present-day [Russia](/source/Russia))
| death_date        = 
| death_place       = 
| citizenship       = [American](/source/United_States)
| ethnicity         = 
| field             = [Mathematics](/source/Mathematics)
| work_institutions = [Yale University](/source/Yale_University)
| alma_mater        = [Saint Petersburg State University](/source/Saint_Petersburg_State_University) <br /> [Yale University](/source/Yale_University)
| doctoral_advisor  = [Howard Garland](/source/Howard_Garland)
| doctoral_students = [Pavel Etingof](/source/Pavel_Etingof) <br /> [Mikhail Khovanov](/source/Mikhail_Khovanov) <br /> [Alexander Kirillov, Jr.](/source/Alexander_Kirillov%2C_Jr.)
| known_for         = 
| author_abbrev_bot = 
| author_abbrev_zoo = 
| influences        = 
| influenced        = 
| prizes            = 
| footnotes         = 
| signature         =  
}}

'''Igor Borisovich Frenkel''' ({{langx|ru|Игорь Борисович Френкель}}; born 22 April 1952) is a Russian-American mathematician at [Yale University](/source/Yale_University) working in [representation theory](/source/representation_theory) and [mathematical physics](/source/mathematical_physics).

Frenkel emigrated to the United States in 1979. He received his PhD from [Yale University](/source/Yale_University) in 1980<!-- under the direction of [Howard Garland](/source/Howard_Garland) --> with a dissertation on the "Orbital Theory for Affine Lie Algebras".  He held positions at the [IAS](/source/Institute_for_Advanced_Study) and [MSRI](/source/Mathematical_Sciences_Research_Institute), and a tenured professorship at [Rutgers University](/source/Rutgers_University), before taking his current job of tenured professor at [Yale University](/source/Yale_University). He was elected to the [National Academy of Sciences](/source/National_Academy_of_Sciences) in 2018.<ref>{{Cite web|url=https://news.yale.edu/2018/05/01/six-yale-professors-elected-national-academy-sciences|title = Six Yale professors elected to National Academy of Sciences|date = May 2018}}</ref> He is also a Fellow of the [American Academy of Arts and Sciences](/source/American_Academy_of_Arts_and_Sciences).<ref>{{Cite web|url=https://news.yale.edu/2018/05/01/six-yale-professors-elected-national-academy-sciences|title = Six Yale professors elected to National Academy of Sciences|date = May 2018}}</ref>

==Mathematical work==

In collaboration with [James Lepowsky](/source/James_Lepowsky) and [Arne Meurman](/source/Arne_Meurman), he constructed the [monster vertex algebra](/source/monster_vertex_algebra), a vertex algebra which provides a representation of the [monster group](/source/monster_group).<ref>{{cite book |last1=Frenkel |first1=Igor |last2=Lepowsky |first2=James |last3=Meurman |first3=Arne |title=Vertex operator algebras and the Monster |series=Pure and Applied Mathematics |volume=134 |year=1988 |publisher=Academic Press |location=Boston |isbn= 0-12-267065-5}}</ref><ref>{{cite journal|title=Review: Igor Frenkel, James Lepowsky and Arne Meurman,''Vertex operator algebras and the Monster''|author=Ogg, Andrew|journal=Bull. Amer. Math. Soc. (N.S.)|year=1991|volume=25|issue=2|pages=425–432|url=http://projecteuclid.org/euclid.bams/1183657192|doi=10.1090/s0273-0979-1991-16086-6|doi-access=free}}</ref>

Around 1990, as a member of the School of Mathematics at the [Institute for Advanced Study](/source/Institute_for_Advanced_Study), Frenkel worked on the mathematical [theory of knots](/source/theory_of_knots), hoping to develop a theory in which the knot would be seen as a physical object. He continued to develop the idea with his student [Mikhail Khovanov](/source/Mikhail_Khovanov), and their collaboration ultimately led to the discovery of [Khovanov homology](/source/Khovanov_homology), a refinement of the [Jones polynomial](/source/Jones_polynomial), in 2002.<ref>{{Citation | last1 = Witten | first1 = Edward | title = Knots and Quantum Theory | newspaper = The Institute Letter | date = Spring 2011 | url = http://www.sns.ias.edu/~witten/papers/KnotsandPhysics.pdf | access-date = 17 August 2011 | url-status = dead | archive-url = https://web.archive.org/web/20110927094941/http://www.sns.ias.edu/~witten/papers/KnotsandPhysics.pdf | archive-date = 27 September 2011 }}</ref>

A detailed description of Igor Frenkel's research over the years can be found in {{cite web |url=http://www.math.sunysb.edu/~frenkel60/Frenkel/Conference.html |title=Perspectives in Representation Theory }}

==References==

{{Reflist}}

==External links==
*[http://users.math.yale.edu/public_html/People/frenkel.html Home page]
*{{MathGenealogy |id=14975}}

{{Authority control}}

{{DEFAULTSORT:Frenkel, Igor}}
Category:1952 births
Category:Living people
Category:20th-century American mathematicians
Category:Rutgers University faculty
Category:Yale University faculty
Category:Mathematicians from Saint Petersburg
Category:Fellows of the American Academy of Arts and Sciences
Category:Members of the United States National Academy of Sciences
Category:Yale University alumni

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{{US-mathematician-stub}}

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Adapted from the Wikipedia article [Igor Frenkel](https://en.wikipedia.org/wiki/Igor_Frenkel) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Igor_Frenkel?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.