Edward Frenkel
Encyclopedia
Edward Frenkel is a mathematician
working in representation theory
, algebraic geometry
, and mathematical physics
. He is currently Professor of Mathematics at University of California, Berkeley
.
. While a student there, he attended the seminar of Israel Gelfand
and worked with Boris Feigin and Dmitry Fuchs. After receiving his college degree in 1989, he was first invited to Harvard University
as a Visiting Professor, and a year later he enrolled as a graduate student at Harvard. He received his Ph.D. from Harvard University
in 1991, after one year of study, under the direction of Boris Feigin and Joseph Bernstein
. He was a Junior Fellow at the Harvard Society of Fellows
from 1991 to 1994, and served as Associate Professor at Harvard from 1994 to 1997. He has been Professor of Mathematics at University of California, Berkeley
since 1997.
of an affine Kac-Moody algebra. The last result, often referred to as Feigin-Frenkel isomorphism, has been used by Alexander Beilinson
and Vladimir Drinfeld in their work on the Geometric Langlands correspondence. Together with Nicolai Reshetikhin
, Frenkel introduced deformations of W-algebras and q-characters of representations of quantum affine algebras.
Frenkel's recent work has focused on the Langlands program
and its connections to representation theory
, integrable systems, geometry
, and physics
. Together with Dennis Gaitsgory
and Kari Vilonen, he has proved the geometric Langlands conjecture for GL(n). His joint work with Robert Langlands
and Ngô Bảo Châu
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
) connections between the Geometric Langlands correspondence and dualities in quantum field theory. Frenkel's Erdős number is three.
. 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
on December 1, 2010 caused some controversy.
He has also written (with Thomas Farber) a screenplay "The Two-Body Problem".
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
working in representation theory
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 studiesmodules over these abstract algebraic structures...
, algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, and mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
. He is currently Professor of Mathematics at University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
.
Biography
Frenkel was not admitted to Moscow State University because of discrimination against Jews and enrolled instead in the Applied Mathematics program at the Gubkin University of Oil and GasGubkin Russian State University of Oil and Gas
The Gubkin Russian State University of Oil and Gas is a university in Moscow. The university was founded on 17 April 1930 and is named after the geologist Ivan Gubkin. The university is affectionally known as Kerosinka , meaning "kerosene stove"...
. While a student there, he attended the seminar of Israel Gelfand
Israel Gelfand
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand was a Soviet mathematician who made major contributions to many branches of mathematics, including group theory, representation theory and functional analysis...
and worked with Boris Feigin and Dmitry Fuchs. After receiving his college degree in 1989, he was first invited to Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
as a Visiting Professor, and a year later he enrolled as a graduate student at Harvard. He received his Ph.D. from Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
in 1991, after one year of study, under the direction of Boris Feigin and Joseph Bernstein
Joseph Bernstein
Joseph Bernstein is an Israeli mathematician working at Tel Aviv University. He works in algebraic geometry, representation theory, and number theory....
. He was a Junior Fellow at the Harvard Society of Fellows
Harvard Society of Fellows
The Harvard Society of Fellows is a group of scholars selected at the beginning of their careers by Harvard University for extraordinary scholarly potential, upon whom distinctive academic and intellectual opportunities are bestowed in order to foster their individual growth and intellectual...
from 1991 to 1994, and served as Associate Professor at Harvard from 1994 to 1997. He has been Professor of Mathematics at University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
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 algebraUniversal enveloping algebra
In mathematics, for any Lie algebra L one can construct its universal enveloping algebra U. This construction passes from the non-associative structure L to a unital associative algebra which captures the important properties of L.Any associative algebra A over the field K becomes a Lie algebra...
of an affine Kac-Moody algebra. The last result, often referred to as Feigin-Frenkel isomorphism, has been used by Alexander Beilinson
Alexander Beilinson
Alexander A. Beilinson 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...
and Vladimir Drinfeld in their work on the Geometric Langlands correspondence. Together with Nicolai Reshetikhin
Nicolai Reshetikhin
Nicolai Yuryevich Reshetikhin is a mathematical physicist, currently a professor of mathematics at the University of California, Berkeley and a professor of mathematical physics at the University of Amsterdam. His research is in the fields of low-dimensional topology, representation theory, and...
, Frenkel introduced deformations of W-algebras and q-characters of representations of quantum affine algebras.
Frenkel's recent work has focused on the Langlands program
Langlands program
The Langlands program is a web of far-reaching and influential conjectures that relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. It was proposed by ....
and its connections to representation theory
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 studiesmodules over these abstract algebraic structures...
, integrable systems, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
. Together with Dennis Gaitsgory
Dennis Gaitsgory
Dennis Gaitsgory is a mathematician at Harvard University known for his research on the geometric Langlands program. Born in what is now Moldova, he grew up in Tajikistan, before studying at Tel Aviv University under Joseph Bernstein. He received his doctorate in 1997 for a thesis entitled...
and Kari Vilonen, he has proved the geometric Langlands conjecture for GL(n). His joint work with Robert Langlands
Robert Langlands
Robert Phelan Langlands is a mathematician, best known as the founder of the Langlands program. He is an emeritus professor at the Institute for Advanced Study...
and Ngô Bảo Châu
Ngo Bao Chau
Ngô Bảo Châu is a Vietnamese and 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 Vietnamese to receive the Fields Medal.- Biography :Chau was born in 1972, the...
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
Edward Witten is an American theoretical physicist with a focus on mathematical physics who is currently a professor of Mathematical Physics at the Institute for Advanced Study....
) connections between the Geometric Langlands correspondence and dualities in quantum field theory. Frenkel's Erdős number is three.
Awards
Frenkel was the first recipient of the Hermann Weyl Prize in 2002. Among his other awards are Packard Fellowship in Science and Engineering and Chaire d'Excellence from Fondation Sciences mathématiques de Paris.Filmmaking
Frenkel has co-produced, co-directed (with Reine Graves) and played the lead 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 MishimaYukio Mishima
was the pen name of , a Japanese author, poet, playwright, actor and film director, also remembered for his ritual suicide by seppuku after a failed coup d'état...
. 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, California
Berkeley is a city on the east shore of the San Francisco Bay in Northern California, United States. Its neighbors to the south are the cities of Oakland and Emeryville. To the north is the city of Albany and the unincorporated community of Kensington...
on December 1, 2010 caused some controversy.
He has also written (with Thomas Farber) a screenplay "The Two-Body Problem".
Select Publications
- E. Frenkel: Langlands Correspondence for Loop Groups, Cambridge Studies in Advanced Mathematics 103, Cambridge University Press 2007, ISBN 978-0-521-85443-6.
- E. Frenkel and D. Ben-Zvi: Vertex Algebras and Algebraic Curves, Mathematical Surveys and Monographs 88, Second Edition, American Mathematical Society 2004, ISBN 0-8218-3674-9.
- E. Frenkel, D. Gaitsgory and K. Vilonen: On the geometric Langlands conjecture 2000.
- E. Frenkel: Recent Advances in the Langlands Program 2003.
- E. Frenkel: Lectures on the Langlands Program and Conformal Field Theory Les Houches 2005.
- E. Frenkel and E. Witten: Geometric Endoscopy and Mirror Symmetry 2007.
- E. Frenkel: Gauge Theory and Langlands Duality Séminaire Bourbaki 2009.
- 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.