Langlands Correspondence for Loop Groups ICM Edition

Langlands Correspondence for Loop Groups ICM Edition The Langlands Program was conceived initially as a bridge between Number Theory and Automorphic Representations and has now expanded into such areas as Geometry and Quantum Field Theory tying togeth

The Langlands Program was conceived initially as a bridge between Number Theory and Automorphic Representations, and has now expanded into such areas as Geometry and Quantum Field Theory, tying together seemingly unrelated disciplines into a web of tantalizing conjectures A new chapter to this grand project is provided in this book It develops the geometric Langlands CorThe Langlands Program was conceived initially as a bridge between Number Theory and Automorphic Representations, and has now expanded into such areas as Geometry and Quantum Field Theory, tying together seemingly unrelated disciplines into a web of tantalizing conjectures A new chapter to this grand project is provided in this book It develops the geometric Langlands Correspondence for Loop Groups, a new approach, from a unique perspective offered by affine Kac Moody algebras The theory offers fresh insights into the world of Langlands dualities, with many applications to Representation Theory of Infinite dimensional Algebras, and Quantum Field Theory This accessible text builds the theory from scratch, with all necessary concepts defined and the essential results proved along the way Based on courses taught at Berkeley, the book provides many open problems which could form the basis for future research, and is accessible to advanced undergraduate students and beginning graduate students.

  • Langlands Correspondence for Loop Groups ICM Edition Best Download || [Edward Frenkel]
    316 Edward Frenkel
Langlands Correspondence for Loop Groups ICM Edition

  1. Edward Frenkel Russian , Edvard Frenkel born May 2, 1968 is a mathematician working in representation theory, algebraic geometry, and mathematical physics He is a professor of mathematics at University of California, Berkeley.Frenkel grew up in Kolomna, Russia to a family of Russian Jews 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 1 He 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 Gas 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 at Harvard University in 1991, after one year of study, under the direction of Joseph Bernstein He was a Junior Fellow at the Harvard Society of Fellows 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 since 1997.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 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 Ng B o Ch u 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 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 Y koku by the Japanese writer Yukio Mishima 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.Frenkel s book Love and Math The Heart of Hidden Reality was published in October 2013.

651 Reply to “Langlands Correspondence for Loop Groups ICM Edition”

Leave a Reply

Your email address will not be published. Required fields are marked *