{{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, Soviet Union (present-day Russia) | death_date = | death_place = | citizenship = American | ethnicity = | field = Mathematics | work_institutions = Yale University | alma_mater = Saint Petersburg State University <br /> Yale University | doctoral_advisor = Howard Garland | doctoral_students = Pavel Etingof <br /> Mikhail Khovanov <br /> Alexander Kirillov, 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 working in representation theory and mathematical physics.
Frenkel emigrated to the United States in 1979. He received his PhD from Yale University in 1980<!-- under the direction of Howard Garland --> with a dissertation on the "Orbital Theory for Affine Lie Algebras". He held positions at the IAS and MSRI, and a tenured professorship at Rutgers University, before taking his current job of tenured professor at Yale University. He was elected to the 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.<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 and Arne Meurman, he constructed the monster vertex algebra, a vertex algebra which provides a representation of the 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, Frenkel worked on the mathematical 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, and their collaboration ultimately led to the discovery of Khovanov homology, a refinement of the 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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