Edward Frenkel
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Edward Vladimirovich Frenkel (; born May 2, 1968) is a Russian-American
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, structure, space, models, and change. History On ...
working in
representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...
,
algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
, and
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 ...
. He is a professor of mathematics at
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 ...
, a member of the
American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...
, and author of the bestselling book ''
Love and Math Love and Math is a book about mathematics written by Edward Frenkel which was published in October 2013. It was a ''New York Times'' bestseller, and was the 2015 winner of the Euler Book Prize. As of February 2016, it has been published in 16 langua ...
''.


Biography

Edward Frenkel was born on May 2, 1968, in
Kolomna Kolomna ( rus, Колóмна, p=kɐˈlomnə) is a historical types of inhabited localities in Russia, city in Moscow Oblast, Russia, situated at the confluence of the Moskva River, Moskva and Oka Rivers, (by rail) southeast of Moscow. Populati ...
,
Russia Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...
, which was then part of the
Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...
. His father is of Jewish descent and his mother is Russian. As a high school student he studied higher mathematics privately with Evgeny Evgenievich Petrov, although his initial interest was in quantum physics rather than mathematics. He was not admitted to
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 ...
because of discrimination against Jews and enrolled instead in the applied mathematics program at the Gubkin University of Oil and Gas. While a student there, he attended the seminar of
Israel Gelfand Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand ( yi, ישראל געלפֿאַנד, russian: Изра́иль Моисе́евич Гельфа́нд, uk, Ізраїль Мойсейович Гел ...
and worked with
Boris Feigin Boris Lvovich Feigin (russian: Бори́с Льво́вич Фе́йгин) (born 20 November 1953) is a Russian mathematician. His research has spanned representation theory, mathematical physics, algebraic geometry, Lie groups and Lie algebra ...
and
Dmitry Fuchs Dmitry Borisovich Fuchs (Дмитрий Борисович Фукс, born 30 September 1939, Kazan, Tatar Autonomous Soviet Socialist Republic) is a Russian-American mathematician, specializing in the representation theory of infinite-dimensional ...
. After receiving his degree in 1989, he was first invited to
Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
as a visiting professor, and a year later he enrolled as a graduate student at Harvard. He received his Ph.D. at
Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
in 1991, after one year of study, under the direction of Boris Feigin and
Joseph Bernstein Joseph Bernstein (sometimes spelled I. N. Bernshtein; he, יוס(י)ף נאומוביץ ברנשטיין; russian: Иосиф Наумович Бернштейн; born 18 April 1945) is a Soviet-born Israeli mathematician working at Tel Aviv Univ ...
. He was a Junior Fellow at the
Harvard Society of Fellows The Society of Fellows is a group of scholars selected at the beginnings of their careers by Harvard University for their potential to advance academic wisdom, upon whom are bestowed distinctive opportunities to foster their individual and intell ...
from 1991 to 1994, and served as an associate professor at Harvard from 1994 to 1997. He has been a professor of mathematics at
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 ...
, since 1997.


Mathematical work

Jointly with Boris Feigin, Frenkel constructed the free field realizations of affine Kac–Moody algebras (these are also known as Wakimoto modules), defined the quantum Drinfeld-Sokolov reduction, and described the center of the
universal enveloping algebra In mathematics, the universal enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal enveloping algebras are used in the representati ...
of an affine Kac–Moody algebra. The last result, often referred to as Feigin–Frenkel isomorphism, has been used by
Alexander Beilinson Alexander A. Beilinson (born 1957) is the David and Mary Winton Green University professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1 ...
and
Vladimir Drinfeld Vladimir Gershonovich Drinfeld ( uk, Володи́мир Ге́ршонович Дрінфельд; russian: Влади́мир Ге́ршонович Дри́нфельд; born February 14, 1954), surname also romanized as Drinfel'd, is a renowne ...
in their work on the
geometric Langlands correspondence In mathematics, the geometric Langlands correspondence is a reformulation of the Langlands correspondence obtained by replacing the number fields appearing in the original number theoretic version by function fields and applying techniques from al ...
. Together with
Nicolai Reshetikhin Nicolai Yuryevich Reshetikhin (russian: Николай Юрьевич Решетихин, born October 10, 1958 in Leningrad, Soviet Union) is a mathematical physicist, currently a professor of mathematics at Tsinghua University, China and a profe ...
, Frenkel introduced deformations of W-algebras and q-characters of representations of
quantum affine algebra In mathematics, a quantum affine algebra (or affine quantum group) is a Hopf algebra that is a ''q''-deformation of the universal enveloping algebra of an affine Lie algebra. They were introduced independently by and as a special case of their g ...
s. Frenkel's recent work has focused on the
Langlands program In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by , it seeks to relate Galois groups in algebraic num ...
and its connections to
representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...
,
integrable system In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first ...
s,
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, and
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
. Together with
Dennis Gaitsgory Dennis Gaitsgory is a professor of mathematics at Harvard University known for his research on the geometric Langlands program. Born in Chișinău, now in Moldova, he grew up in Tajikistan, before studying at Tel Aviv University under Joseph Ber ...
and Kari Vilonen, he has proved the geometric Langlands conjecture for
GL(n) In mathematics, the general linear group of degree ''n'' is the set of invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, ...
. His joint work with
Robert Langlands Robert Phelan Langlands, (; born October 6, 1936) is a Canadian mathematician. He is best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study o ...
and
Ngô Bảo Châu Ngô Bảo Châu (, born June 28, 1972) is a Vietnamese-French mathematician at the University of Chicago, best known for proving the fundamental lemma for automorphic forms (proposed by Robert Langlands and Diana Shelstad). He is the first Vie ...
suggested a new approach to the functoriality of automorphic representations and trace formulas. He has also been investigating (in particular, in a joint work with
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, q ...
) connections between the
geometric Langlands correspondence In mathematics, the geometric Langlands correspondence is a reformulation of the Langlands correspondence obtained by replacing the number fields appearing in the original number theoretic version by function fields and applying techniques from al ...
and dualities in
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
.


Awards

Frenkel was the first recipient of the
Hermann Weyl Prize Hermann or Herrmann may refer to: * Hermann (name), list of people with this name * Arminius, chieftain of the Germanic Cherusci tribe in the 1st century, known as Hermann in the German language * Éditions Hermann, French publisher * Hermann, Miss ...
in 2002. Among his other awards are Packard Fellowship in Science and Engineering and Chaire d'Excellence from Fondation Sciences mathématiques de Paris. In 2013, he became a
fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...
of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
, for "contributions to representation theory, conformal field theory, affine Lie algebras, and quantum field theory". In 2014, Frenkel was elected to the
American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...
.


Filmmaking

Frenkel has co-produced, co-directed (with Reine Graves) and starred in a short film ''Rites of Love and Math'', a homage to the film '' Rite of Love and Death'' (also known as '' Yûkoku'') by the Japanese writer
Yukio Mishima , born , was a Japanese author, poet, playwright, actor, model, Shintoist, Nationalism, nationalist, and founder of the , an unarmed civilian militia. Mishima is considered one of the most important Japanese authors of the 20th century. He was ...
. The film premiered in Paris in April, 2010 and was in the official competition of the Sitges International Film Festival in October, 2010. The screening of ''Rites of Love and Math'' in
Berkeley Berkeley most often refers to: *Berkeley, California, a city in the United States **University of California, Berkeley, a public university in Berkeley, California * George Berkeley (1685–1753), Anglo-Irish philosopher Berkeley may also refer ...
on December 1, 2010 caused some controversy. He has also written (with Thomas Farber) a screenplay ''The Two-Body Problem''. He has appeared on the ''
Numberphile ''Numberphile'' is an educational YouTube channel featuring videos that explore topics from a variety of fields of mathematics. In the early days of the channel, each video focused on a specific number, but the channel has since expanded its s ...
''
YouTube YouTube is a global online video platform, online video sharing and social media, social media platform headquartered in San Bruno, California. It was launched on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim. It is owned by ...
series, created by
Brady Haran Brady John Haran (born 18 June 1976) is an Australian-British independent filmmaker and video journalist who produces educational videos and documentary films for his YouTube channels, the most notable being ''Periodic Videos'' and ''Number ...
.


''Love and Math''

Frenkel's book ''Love and Math: The Heart of Hidden Reality'' was published in October 2013. It was a ''New York Times'' bestseller, and was the 2015 winner of the
Euler Book Prize The Euler Book Prize is an award named after Swiss mathematician and physicist Leonhard Euler (1707-1783) and given annually at the Joint Mathematics Meetings by the Mathematical Association of America to an outstanding book in mathematics that is ...
. As of February 2016, it has been published in 16 languages.Frenkel's website
/ref> In a review published in ''
The New York Review of Books ''The New York Review of Books'' (or ''NYREV'' or ''NYRB'') is a semi-monthly magazine with articles on literature, culture, economics, science and current affairs. Published in New York City, it is inspired by the idea that the discussion of i ...
'', Jim Holt called ''Love and Math'' a "winsome new memoir" which is "three things: a Platonic love letter to mathematics; an attempt to give the layman some idea of its most magnificent drama-in-progress; and an autobiographical account, by turns inspiring and droll, of how the author himself came to be a leading player in that drama.” ''
The New York Times ''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid ...
'' review called the book "powerful, passionate and inspiring."
Keith Devlin Keith J. Devlin (born 16 March 1947) is a British mathematician and popular science writer. Since 1987 he has lived in the United States. He has dual British-American citizenship.
wrote in ''
The Huffington Post ''HuffPost'' (formerly ''The Huffington Post'' until 2017 and sometimes abbreviated ''HuffPo'') is an American progressive news website, with localized and international editions. The site offers news, satire, blogs, and original content, and ...
'': "With every page, I found my mind's eye conjuring up a fictional image of the book's author, writing by candlelight in the depths of the Siberian winter like
Omar Sharif Omar Sharif ( ar, عمر الشريف ; born Michel Yusef Dimitri Chalhoub , 10 April 193210 July 2015) was an Egyptian actor, generally regarded as one of his country's greatest male film stars. He began his career in his native country in the ...
's Doctor Zhivago in the David Lean movie adaptation of Pasternak's famous novel. ''Love and Math'' is Edward Frenkel's ''Lara'' poems... As is true for all the great Russian novels, you will find in Frenkel's tale that one person's individual story of love and overcoming adversity provides both a penetrating lens on society and a revealing mirror into the human mind."
Peter Woit Peter Woit (; born September 11, 1957) is an American theoretical physicist. He is a senior lecturer in the Mathematics department at Columbia University. Woit, a critic of string theory, has published a book ''Not Even Wrong'' (2006) and writ ...
, author of ''Not Even Wrong'', wrote in a blog post:
The ''Love'' of the title is much more about love of mathematics than love of another person, as Frenkel provides a detailed story of what it is like to fall in love with mathematics, then pursue this deeply, ending up doing mathematics at the highest level.


Select publications

* E. Frenkel, D. Gaitsgory and K. Vilonen
''On the geometric Langlands conjecture''
2000. * * E. Frenkel and D. Ben-Zvi: ''Vertex Algebras and Algebraic Curves'', Mathematical Surveys and Monographs 88, Second Edition, American Mathematical Society 2004, . * * * E. Frenkel and E. Witten
''Geometric Endoscopy and Mirror Symmetry''
2007. * * E. Frenkel, R. Langlands and B. C. Ngô
''Formule des Traces et Fonctorialité: le Début d'un Programme''
2010. * E. Frenkel and B. C. Ngô
''Geometrization of Trace Formulas''
2010. * *


References


Citations


Sources

* * * * * * * * *


External links

* * *
Official Web site of Rites of Love and Math
{{DEFAULTSORT:Frenkel, Edward Living people 20th-century American mathematicians 21st-century American mathematicians Mathematics popularizers 1968 births Harvard University alumni University of California, Berkeley College of Letters and Science faculty American people of Russian-Jewish descent People from Kolomna Fellows of the American Mathematical Society Harvard Fellows Fellows of the American Academy of Arts and Sciences Russian people of Jewish descent