Edward Frenkel
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Mathematician working in representation theory, algebraic geometry, and mathematical physics
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Edward Frenkelmathematics Degrees
Mathematics
#147
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#349
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#63
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Mathematical Physics
#10
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#14
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#4
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Algebraic Geometry
#36
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#37
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#8
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Measure Theory
#2333
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#2789
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#658
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Mathematics
Why Is Edward Frenkel Influential?
(Suggest an Edit or Addition)According to Wikipedia, Edward Vladimirovich Frenkel is a Russian-American mathematician working in representation theory, algebraic geometry, and mathematical physics. He is a professor of mathematics at University of California Berkeley, a member of the American Academy of Arts and Sciences, and author of the bestselling book Love and Math.
Edward Frenkel's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Vertex Algebras and Algebraic Curves (2000) (872)
- AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS (1992) (330)
- The q-characters of representations of quantum affine algebras and deformations of W-algebras (1998) (330)
- Quantization of the Drinfeld-Sokolov reduction (1990) (273)
- Gaudin model, Bethe Ansatz and critical level (1994) (273)
- Affine Kac-Moody algebras and semi-infinite flag manifolds (1990) (243)
- Characters and fusion rules forW-algebras via quantized Drinfeld-Sokolov reduction (1992) (233)
- Lectures on the Langlands program and conformal field theory (2005) (216)
- Langlands Correspondence for Loop Groups (2007) (213)
- Combinatorics of q-Characters of Finite-Dimensional Representations of Quantum Affine Algebras (1999) (207)
- Quantum-algebras and elliptic algebras (1995) (195)
- W_{1+\infty} and W(gl_N) with central charge N (1994) (193)
- Lectures on Wakimoto modules, opers and the center at the critical level (2002) (167)
- Integrals of motion and quantum groups (1993) (150)
- Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1 (1995) (142)
- Local geometric Langlands correspondence and affine Kac-Moody algebras (2005) (139)
- Two-dimensional black hole as a topological coset model of c = 1 string theory (1993) (132)
- Deformations of W-algebras associated to simple Lie algebras (1997) (124)
- A family of representations of affine Lie algebras (1988) (119)
- Affine Algebras, Langlands Duality and Bethe Ansatz (1995) (111)
- BAXTER'S RELATIONS AND SPECTRA OF QUANTUM INTEGRABLE MODELS (2013) (109)
- Representations of affine Kac-Moody algebras, bosonization and resolutions (1990) (103)
- Deformations of the KdV hierarchy and related soliton equations (1995) (89)
- Gaudin models with irregular singularities (2006) (88)
- Quantum $q$-Langlands Correspondence (2017) (84)
- Whittaker patterns in the geometry of moduli spaces of bundles on curves (1999) (79)
- Drinfeld–Sokolov Reduction for Difference Operators and Deformations of -Algebras¶I. The Case of Virasoro Algebra (1997) (77)
- Surface operators and separation of variables (2015) (73)
- Recent advances in the Langlands Program (2003) (66)
- Opers with irregular singularity and spectra of the shift of argument subalgebra (2007) (66)
- A rigid irregular connection on the projective line (2009) (63)
- Quantization of soliton systems and Langlands duality (2007) (61)
- Geometric Endoscopy and Mirror Symmetry (2007) (59)
- Opers on the projective line, flag manifolds and Bethe Ansatz (2003) (58)
- Duality in W-algebras (1991) (55)
- Gaudin Model and Opers (2004) (55)
- Instantons beyond topological theory. I (2006) (53)
- Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities (1993) (52)
- Semi-infinite Weil complex and the Virasoro algebra (1991) (51)
- Integrable Systems and Quantum Groups (1996) (50)
- Thermodynamic Bethe Ansatz and Dilogarithm Identities I (1995) (49)
- Towards Deformed Chiral Algebras (1997) (48)
- D-modules on the affine Grassmannian and representations of affine Kac-Moody algebras (2003) (47)
- Spectra of Quantum KdV Hamiltonians, Langlands Duality, and Affine Opers (2016) (47)
- Quantum Affine Algebras and Deformations of the Virasoro and W-Algebras (2019) (46)
- Free field realizations in representation theory and conformal field theory (1994) (46)
- Mirror Symmetry in Two Steps: A–I–B (2005) (45)
- Localization of g^-modules on the affine Grassmannian (2005) (43)
- Gauge Theory and Langlands Duality (2009) (43)
- Quantum Langlands dualities of boundary conditions, $D$-modules, and conformal blocks (2018) (41)
- Spectral curves, opers and integrable systems (1999) (41)
- Soliton equations, vertex operators, and simple singularities (2009) (40)
- Twisted Modules over Vertex Algebras on Algebraic Curves (2001) (39)
- GEOMETRIC REALIZATION OF THE SEGAL-SUGAWARA CONSTRUCTION (2003) (39)
- Geometric realization of Whittaker functions and the Langlands conjecture (1997) (37)
- Free field resolutions in affine Toda field theories (1992) (36)
- Affine Kac-Moody algebras at the critical level and quantum Drinfeld-Sokolov reduction (1991) (35)
- D-modules on the affine flag variety and representations of affine Kac-Moody algebras (2007) (35)
- Notes on instantons in topological field theory and beyond (2007) (34)
- W -Algebras and Langlands-Drinfeld Correspondence (1992) (34)
- On the geometric Langlands conjecture (2000) (32)
- Love and Math: The Heart of Hidden Reality (2013) (31)
- Gerbal Representations of Double Loop Groups (2008) (31)
- CHIRAL DE RHAM COMPLEX AND ORBIFOLDS (2003) (29)
- Langlands Duality for Finite-Dimensional Representations of Quantum Affine Algebras (2009) (28)
- Cohomology of the commutator subgroup of the braid group (1988) (28)
- Weyl modules and opers without monodromy (2007) (25)
- The q-Characters at Roots of Unity (2001) (24)
- Local Geometric Langlands Correspondence: the Spherical Case (2007) (23)
- Determinant formulas for the free field representations of the Virasoro and Kac-Moody algebras (1992) (22)
- Fusion and convolution: applications to affine Kac-Moody algebras at the critical level (2005) (22)
- Kac-Moody groups and integrability of soliton equations (1993) (21)
- Geometrization of trace formulas (2010) (21)
- Langlands duality for representations of quantum groups (2008) (20)
- The hopf algebra rep $$U_q \widehat{\mathfrak{g}\mathfrak{l}}_\infty $$ (2002) (19)
- Equivalence of Two Approaches to Integrable Hierarchies of KdV type (1997) (19)
- Geometric realizations of Wakimoto modules at the critical level (2006) (19)
- Any flat bundle on a punctured disc has an oper structure (2008) (18)
- Self-extensions of Verma modules and differential forms on opers (2004) (18)
- The Hopf algebra Rep $ U_{q} \widehat{\frak g \frak l}_\infty $ (2002) (17)
- Integrable Hierarchies and Wakimoto Modules (1999) (17)
- Geometric interpretation of the Poisson structure in affine Toda field theories (1996) (16)
- Localization of \(\hat{\mathfrak{g}}\)-modules on the Affine Grassmannian (2009) (14)
- Geometric Langlands Correspondence Near Opers (2013) (14)
- Dilogarithm identities, q-difference equations and the Virasoro algebra (1992) (14)
- An analytic version of the Langlands correspondence for complex curves (2019) (13)
- Ramifications of the Geometric Langlands Program (2006) (13)
- Intermediate Wakimoto modules for affine sl ( n + 1 , C ) (2004) (13)
- Quantum Langlands duality of representations of ${\mathcal{W}}$ -algebras (2018) (12)
- Folded quantum integrable models and deformed W-algebras (2021) (12)
- Bosonic ghost system and the Virasoro algebra (1990) (12)
- Representation Theory and Complex Analysis (2008) (11)
- Affine Kac-Moody algebras, integrable systems and their deformations (2003) (10)
- Langlands Program, Trace Formulas, and their Geometrization (2012) (10)
- Crystal bases, dilogarithm identities and torsion in algebraic $K$-theory (1995) (10)
- Equivalence of Two Approaches to the mKdV Hierarchies (1996) (9)
- Gromov-Witten gauge theory (2009) (8)
- Free field realization II (2004) (8)
- Five lectures on Soliton equations (1997) (8)
- Crystal bases, dilogarithm identities and torsion in algebraic K-groups (1993) (7)
- Generalized KDV flows and nilpotent subgroups of affine Kac-Moody groups (1993) (6)
- On strictly sparse subsets of a free group. (2005) (5)
- Is There an Analytic Theory of Automorphic Functions for Complex Algebraic Curves? (2018) (5)
- Amalgamated products of groups: measures of random normal forms (2011) (5)
- $q$-opers, $QQ$-systems, and Bethe Ansatz (2020) (4)
- Semi-infinite Weil complex and the Virasoro algebra (1991) (4)
- with central chargeN (1995) (4)
- Hecke operators and analytic Langlands correspondence for curves over local fields (2021) (3)
- Analytic Langlands correspondence for PGL(2) on P^1 with parabolic structures over local fields (2021) (3)
- On the Endomorphisms of Weyl Modules over Affine Kac–Moody Algebras at the Critical Level (2008) (3)
- Opinion: two views: how much math do scientists need? (2013) (3)
- Applications of representation theory to harmonic analysis of Lie groups (and vice versa) (2008) (2)
- The Hopf algebra $Rep U_q \hat{gl}_\infty$ (2001) (2)
- AI Safety (2018) (1)
- Mathematics, Love, and Tattoos (2012) (1)
- CLASS FIELD THEORY, ITS THREE MAIN GENERALISATIONS, AND APPLICATIONS (2019) (1)
- Verma modules of critical level and differential forms on opers (2004) (1)
- Jet Schemes of Locally Complete Intersection Canonical Singularities by Mircea Mustat¸ˇa with an Appendix (2001) (1)
- W - and Langlands-Drinfeld Correspondence (1995) (1)
- AMS Spring Sectional Sampler (2018) (0)
- A G ] 2 0 Ja n 20 03 GEOMETRIC REALIZATION OF THE SEGAL – SUGAWARA CONSTRUCTION (2018) (0)
- Q A ] 8 M ar 2 00 5 Gaudin model and opers (2004) (0)
- Vertex Lie algebras and classical limits (2004) (0)
- Solving the KZ equations (2004) (0)
- Preprint typeset in JHEP style-HYPER VERSION Surface Operators and Separation of Variables (2015) (0)
- Mathematische Annalen Langlands duality for representations of quantum groups (2011) (0)
- Geometric Langlands Program and Dualities in Quantum Physics (2009) (0)
- AMS Einstein Public Lecture: Imagination and Knowledge (2018) (0)
- Commentary on “An elementary introduction to the Langlands Program” by Steven Gelbart (2011) (0)
- Vertex algebras associated to Lie algebras (2004) (0)
- Vertex algebra bundles: Examples (2004) (0)
- Associativity and operator product expansion (2004) (0)
- Vertex algebra bundles (2004) (0)
- Vertex algebras and moduli spaces II (2004) (0)
- Spectra of Quantum KdV Hamiltonians, Langlands Duality, and Affine Opers (2018) (0)
- DILOGARITHM IDENTITIES , AND TORSION IN ALGEBRAIC K-THEORY (2009) (0)
- Modules over vertex algebras and more examples (2004) (0)
- Applications of the operator product expansion (2004) (0)
- Weyl group symmetry of q-characters (2022) (0)
- Central extensions of reductive groups by K[2] . Spectral curves, opers and integrable systems . Variétés sphériques de type A (2001) (0)
- Quantum Drinfeld–Sokolov reduction and –algebras (2004) (0)
- Surface operators and separation of variables (2016) (0)
- REPRESENTATIONS OF DOUBLE LOOP GROUPS (2008) (0)
- SOLITON EQUATIONS , VERTEX OPERATORS , AND SIMPLE (2009) (0)
- Amalgamated free product of groups: Normal forms and measures (2012) (0)
- DUALITY FOR REPRESENTATIONS OF QUANTUM GROUPS (2008) (0)
- ROBERT LANGLANDS: ABEL LAUREATE 2018 (2018) (0)
- Ju l 2 00 3 CHIRAL DE RHAM COMPLEX AND ORBIFOLDS (0)
- Analytic Langlands correspondence for PGL2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$PGL_2$$\end{document} on P1\ (2022) (0)
- Conformal blocks II (2004) (0)
- A ug 2 00 3 TWISTED MODULES OVER VERTEX ALGEBRAS ON ALGEBRAICCURVES (2004) (0)
- A Brief Introduction to Infinity by Edward (2016) (0)
- Integrable Hierarchies and Wakimoto Realization (1999) (0)
- A ] 3 0 Ju l 2 00 4 Gaudin model and opers (2004) (0)
- Analytic Langlands correspondence for $$PGL_2$$ on $${\mathbb {P}}^1$$ with parabolic structures over local fields (2022) (0)
- Action of internal symmetries (2004) (0)
- Definition of vertex algebras (2004) (0)
- The Hermann Weyl Prize 2014 (2015) (0)
- The Knizhnik–Zamolodchikov equations (2004) (0)
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