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Mathematics

D-Index
56
Citations
10554
World Ranking
741
National Ranking
365

Research.com Recognitions

  • 2014 - Fellow of the American Mathematical Society For contributions to representation theory, conformal field theory, affine Lie algebras, and quantum field theory.
  • 2014 - Fellow of the American Academy of Arts and Sciences
  • 1995 - Fellow of Alfred P. Sloan Foundation

Overview

Edward Frenkel is affiliated with the University of California, Berkeley in the United States. Their research is primarily situated within the field of Mathematics, with a significant focus on Mathematical Physics, Geometry and Topology, and Discrete Mathematics and Combinatorics. Additional areas of interest include Nuclear and High Energy Physics and topics related to General Health Professions.

Their research topics cover:

  • Advanced Algebra and Geometry
  • Algebraic structures and combinatorial models
  • Algebraic Geometry and Number Theory
  • Advanced Combinatorial Mathematics
  • Black Holes and Theoretical Physics
  • Advanced Mathematical Physics Problems
  • Geometry and complex manifolds

Edward Frenkel has published extensively, with a total of 45 works in mathematics-related fields. Their most frequent publication platforms include arXiv (Cornell University) with 7 publications, the Journal of the European Mathematical Society, Communications in Number Theory and Physics, Duke Mathematical Journal, and Communications in Mathematical Physics.

Recent significant papers include:

  • $q$-opers, $QQ$-systems, and Bethe Ansatz, 2023, Journal of the European Mathematical Society
  • Quantum Langlands dualities of boundary conditions, $D$-modules, and conformal blocks, 2020, Communications in Number Theory and Physics
  • An analytic version of the Langlands correspondence for complex curves, 2021, Proceedings of symposia in pure mathematics (co-authored with Pavel Etingof)
  • Hecke operators and analytic Langlands correspondence for curves over local fields, 2023, Duke Mathematical Journal (co-authored with Pavel Etingof)
  • Extended Baxter Relations and QQ-Systems for Quantum Affine Algebras, 2024, Communications in Mathematical Physics

Frequent collaborators include:

  • Pavel Etingof
  • David Kazhdan
  • David Hernandez
  • Peter Koroteev
  • Daniel S. Sage

Edward Frenkel's contributions have been recognized through their election as a Fellow of the American Mathematical Society in 2014 for work in representation theory, conformal field theory, affine Lie algebras, and quantum field theory. In the same year, they were also named a Fellow of the American Academy of Arts and Sciences. Additionally, they received a fellowship from the Alfred P. Sloan Foundation in 1995.

Best Publications

  • Vertex Algebras and Algebraic Curves

    Edward Vladimir Frenkel;David Ben-Zvi

  • Quantization of the Drinfeld-Sokolov reduction

    Boris Feigin;Edward Frenkel

  • Characters and fusion rules for W-algebras via quantized Drinfeld-Sokolov reduction

    Edward Frenkel;Victor Kac;Minoru Wakimoto

  • AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS

    Boris Feigin;Edward Frenkel

  • Gaudin model, Bethe ansatz and critical level

    Boris Feigin;Edward Frenkel;Nikolai Reshetikhin

  • Affine Kac-Moody algebras and semi-infinite flag manifolds

    Boris L. Geigin;Edward V. Frenkel

  • Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1

    Edward Frenkel;Nikolai Reshetikhin

  • Quantum $\scr W$-algebras and elliptic algebras

    Boris Feigin;Edward Frenkel

  • Lectures on the Langlands program and conformal field theory

    Edward Frenkel

  • Combinatorics of q-Characters of Finite-Dimensional Representations of Quantum Affine Algebras

    Edward Frenkel;Evgeny Mukhin

  • with central charge N

    Edward Frenkel;Victor Kac;Andrey Radul;Weiqiang Wang

  • The q-characters of representations of quantum affine algebras and deformations of W-algebras

    Edward Frenkel;Nicolai Reshetikhin

  • Langlands Correspondence for Loop Groups

    Edward Vladimir Frenkel

  • Wakimoto modules, opers and the center at the critical level

    Edward Frenkel

  • Quantum Affine Algebras and Deformations of the Virasoro and W-algebras

    Edward Frenkel;Nikolai Reshetikhin

  • Deformations of W-algebras associated to simple Lie algebras

    Edward Frenkel;Nicolai Reshetikhin

  • A family of representations of affine Lie algebras

    B L Feigin;E V Frenkel

  • Integrals of motion and quantum groups

    Boris Feigin;Edward Frenkel

  • BAXTER'S RELATIONS AND SPECTRA OF QUANTUM INTEGRABLE MODELS

    Edward Frenkel;David Hernandez

  • Quantum W-algebras and Elliptic Algebras

    Boris Feigin;Edward Frenkel

  • Vertex Algebras and Algebraic Curves

    Edward Frenkel

Frequent Co-Authors

Boris Feigin
Boris Feigin Hebrew University of Jerusalem
Dennis Gaitsgory
Dennis Gaitsgory Harvard University
Weiqiang Wang
Weiqiang Wang University of Virginia
Nicolai Reshetikhin
Nicolai Reshetikhin Tsinghua University
David Kazhdan
David Kazhdan Hebrew University of Jerusalem
Nolan R. Wallach
Nolan R. Wallach University of California, San Diego
Andrei Okounkov
Andrei Okounkov Columbia University
Masaki Kashiwara
Masaki Kashiwara Kyoto University
Edward Witten
Edward Witten Institute for Advanced Study

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