Edit Profile (opens in new tab) Frenkel, Edward V. Co-Author Distance Author ID: frenkel.edward-v Published as: Frenkel, Edward; Frenkel, E.; Frenkel, Edward V.; Frenkel’, E. V.; Frenkel’, Edward V.; Frenkel, E. V. more...less Homepage: https://www.edwardfrenkel.com/ External Links: MGP · ORCID · Wikidata · Twitter · Math-Net.Ru · GND · IdRef Videos: carmin.tv Documents Indexed: 114 Publications since 1988, including 7 Books and 8 Additional arXiv Preprints 1 Contribution as Editor Reviewing Activity: 4 Reviews Co-Authors: 46 Co-Authors with 91 Joint Publications 1,520 Co-Co-Authors all top 5 Co-Authors 24 single-authored 21 Feĭgin, Boris L’vovich 11 Gaitsgory, Dennis 7 Hernandez, David 7 Reshetikhin, Nikolai Yu. 6 Kazhdan, David 5 Etingof, Pavel Il’ich 4 Ben-Zvi, David 4 Losev, Andrei S. 4 Szenes, András 3 Mukhin, Evgeny 3 Nekrasov, Nikita Alexandrovich 3 Ngô Bao Châu 3 Teleman, Constantin 3 Vilonen, Kari 2 Averina, Ya. S. 2 Enriquez, Benjamin 2 Kac, Victor 2 Langlands, Robert Phelan 2 Myasnikov, Alexei G. 2 Remeslennikov, Vladimir Nikanorovich 2 Rybnikov, Leonid Grigor’evich 2 Szczesny, Matthew 2 Zhu, Xinwen 1 Aganagic, Mina 1 Alekseev, Anton Yur’evich 1 Arakawa, Tomoyuki 1 Gaiotto, Davide 1 Givental, Alexander Borisovich 1 Gross, Benedict Hyman 1 Gukov, Sergei 1 Koroteev, Peter 1 Milanov, Todor E. 1 Okun’kov, Andreĭ Yur’evich 1 Radul, Andrey 1 Rosso, Marc 1 Sage, Daniel S. 1 Semenov-Tyan-Shanskiĭ, Mikhail Arsen’evich 1 Teschner, Jörg 1 Toledano Laredo, Valerio 1 Tolland, A. J. 1 Wakimoto, Minoru 1 Wang, Weiqiang 1 Webster, Ben 1 Witten, Edward 1 Yakimov, Milen T. 1 Zeitlin, Anton M. all top 5 Serials 15 Communications in Mathematical Physics 6 Duke Mathematical Journal 5 Advances in Mathematics 4 Letters in Mathematical Physics 4 IMRN. International Mathematics Research Notices 3 Journal of the American Mathematical Society 3 Bulletin of the American Mathematical Society. New Series 3 Annals of Mathematics. Second Series 2 Physics Letters. B 2 Compositio Mathematica 2 Mathematical Research Letters 2 Pure and Applied Mathematics Quarterly 2 Mathematical Surveys and Monographs 2 Communications in Number Theory and Physics 1 International Journal of Modern Physics A 1 Mathematical Notes 1 Russian Mathematical Surveys 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Annales des Sciences Mathématiques du Québec 1 Functional Analysis and its Applications 1 Publications Mathématiques 1 Inventiones Mathematicae 1 Mathematische Annalen 1 Transactions of the Moscow Mathematical Society 1 Journal of the Ramanujan Mathematical Society 1 Geometric and Functional Analysis. GAFA 1 Notices of the American Mathematical Society 1 Journal of Algebraic Geometry 1 Journal of Mathematical Sciences (New York) 1 Selecta Mathematica. New Series 1 Representation Theory 1 Vestnik Omskogo Universiteta 1 Journal of the European Mathematical Society (JEMS) 1 Journal of High Energy Physics 1 Moscow Mathematical Journal 1 Journal of the Institute of Mathematics of Jussieu 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Cambridge Studies in Advanced Mathematics 1 Progress in Mathematics 1 Functional Analysis and Other Mathematics 1 Bulletin of Mathematical Sciences all top 5 Fields 68 Nonassociative rings and algebras (17-XX) 47 Quantum theory (81-XX) 36 Algebraic geometry (14-XX) 30 Topological groups, Lie groups (22-XX) 24 Number theory (11-XX) 16 Dynamical systems and ergodic theory (37-XX) 10 Statistical mechanics, structure of matter (82-XX) 8 Partial differential equations (35-XX) 6 History and biography (01-XX) 6 Group theory and generalizations (20-XX) 5 General and overarching topics; collections (00-XX) 3 Differential geometry (53-XX) 2 Associative rings and algebras (16-XX) 2 \(K\)-theory (19-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 Ordinary differential equations (34-XX) 2 Difference and functional equations (39-XX) 2 Probability theory and stochastic processes (60-XX) 1 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Abstract harmonic analysis (43-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 100 Publications have been cited 3,302 times in 1,772 Documents Cited by ▼ Year ▼ Vertex algebras and algebraic curves. 2nd revised and expanded ed. Zbl 1106.17035 Frenkel, Edward; Ben-Zvi, David 242 2004 The \(q\)-characters of representations of quantum affine algebras and deformations of \(W\)-algebras. Zbl 0973.17015 Frenkel, Edward; Reshetikhin, Nicolai 187 1999 Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras. Zbl 0925.17022 Feigin, Boris; Frenkel, Edward 139 1992 Quantization of the Drinfel’d-Sokolov reduction. Zbl 1242.17023 Feigin, Boris; Frenkel, Edward 138 1990 Vertex algebras and algebraic curves. Zbl 0981.17022 Frenkel, Edward; Ben-Zvi, David 134 2001 Gaudin model, Bethe ansatz and critical level. Zbl 0812.35103 Feigin, Boris; Frenkel, Edward; Reshetikhin, Nikolai 131 1994 \({\mathcal W}_{1+\infty}\) and \({\mathcal W}(gl_ N)\) with central charge \(N\). Zbl 0838.17028 Frenkel, Edward; Kac, Victor; Radul, Andrey; Wang, Weiqiang 114 1995 Langlands correspondence for loop groups. Zbl 1133.22009 Frenkel, Edward 110 2007 Combinatorics of \(q\)-characters of finite-dimensional representations of quantum affine algebras. Zbl 1051.17013 Frenkel, Edward; Mukhin, Evgeny 108 2001 Characters and fusion rules for \(W\)-algebras via quantized Drinfeld- Sokolov reduction. Zbl 0768.17008 Frenkel, Edward; Kac, Victor; Wakimoto, Minoru 101 1992 Affine Kac-Moody algebras and semi-infinite flag manifolds. Zbl 0722.17019 Feigin, Boris L.; Frenkel, Edward V. 89 1990 Quantum affine algebras and deformations of the Virasoro and \({\mathcal W}\)-algebras. Zbl 0869.17014 Frenkel, Edward; Reshetikhin, Nikolai 84 1996 Baxter’s relations and spectra of quantum integrable models. Zbl 1332.82022 Frenkel, Edward; Hernandez, David 75 2015 Wakimoto modules, opers and the center at the critical level. Zbl 1129.17014 Frenkel, Edward 74 2005 Quantum \({\mathcal W}\)-algebras and elliptic algebras. Zbl 0871.17007 Feigin, Boris; Frenkel, Edward 67 1996 Deformations of \(W\)-algebras associated to simple Lie algebras. Zbl 0939.17011 Frenkel, Edward; Reshetikhin, Nicolai 61 1998 Representations of affine Kac-Moody algebras, bosonization and resolutions. Zbl 0711.17012 Feigin, Boris L.; Frenkel, Edward V. 56 1990 Gaudin models with irregular singularities. Zbl 1186.81065 Feigin, B.; Frenkel, E.; Toledano Laredo, V. 52 2010 Integrals of motion and quantum groups. Zbl 0885.58034 Feigin, Boris; Frenkel, Edward 49 1996 Quantization of soliton systems and Langlands duality. Zbl 1245.81062 Feigin, Boris; Frenkel, Edward 49 2011 Quantum \(q\)-Langlands correspondence. Zbl 1422.22021 Aganagic, M.; Frenkel, E.; Okounkov, A. 49 2018 Lectures on the Langlands program and conformal field theory. Zbl 1196.11091 Frenkel, Edward 46 2007 Local geometric Langlands correspondence and affine Kac-Moody algebras. Zbl 1184.17011 Frenkel, Edward; Gaitsgory, Dennis 45 2006 Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers. Zbl 1397.81060 Frenkel, Edward; Hernandez, David 38 2018 The Hopf algebra \(\text{Rep\,} U_q \widehat{\mathfrak g\mathfrak l}_\infty\). Zbl 1034.17009 Frenkel, E.; Mukhin, E. 36 2002 Affine algebras, Langlands duality and Bethe ansatz. Zbl 1052.17504 Frenkel, Edward 34 1995 Surface operators and separation of variables. Zbl 1388.81811 Frenkel, Edward; Gukov, Sergei; Teschner, Jörg 34 2016 Opers with irregular singularity and spectra of the shift of argument subalgebra. Zbl 1226.22017 Feigin, Boris; Frenkel, Edward; Rybnikov, Leonid 33 2010 A rigid irregular connection on the projective line. Zbl 1209.14017 Frenkel, Edward; Gross, Benedict 31 2009 Deformations of the KdV hierarchy and related soliton equations. Zbl 0860.17033 Frenkel, Edward 30 1996 Gaudin model and opers. Zbl 1132.17305 Frenkel, Edward 30 2005 Opers on the projective line, flag manifolds and Bethe Ansatz. Zbl 1087.82008 Frenkel, Edward 30 2004 Instantons beyond topological theory. I. Zbl 1230.81050 Frenkel, E.; Losev, A.; Nekrasov, N. 30 2011 Whittaker patterns in the geometry of moduli spaces of bundles on curves. Zbl 1070.11050 Frenkel, E.; Gaitsgory, D.; Vilonen, K. 30 2001 Quantum Langlands dualities of boundary conditions, \(D\)-modules, and conformal blocks. Zbl 1445.14024 Frenkel, Edward; Gaiotto, Davide 30 2020 A family of representations of affine Lie algebras. Zbl 0668.17015 Feigin, B. L.; Frenkel’, Edward V. 27 1988 Duality in \(W\)-algebras. Zbl 0790.17013 Feigin, Boris; Frenkel, Edward 27 1991 Drinfeld-Sokolov reduction for difference operators and deformations of \({\mathcal W}\)-algebras. I: The case of Virasoro algebra. Zbl 0916.17020 Frenkel, E.; Reshetikhin, N.; Semenov-Tian-Shansky, M. A. 26 1998 On the geometric Langlands conjecture. Zbl 1071.11039 Frenkel, E.; Gaitsgory, D.; Vilonen, K. 24 2002 Geometric endoscopy and mirror symmetry. Zbl 1223.14014 Frenkel, Edward; Witten, Edward 24 2008 Semi-infinite Weil complex and the Virasoro algebra. Zbl 0726.17035 Feigin, Boris; Frenkel, Edward 23 1991 Soliton equations, vertex operators, and simple singularities. Zbl 1203.37108 Frenkel, Edward; Givental, Alexander; Milanov, Todor 22 2010 Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities. Zbl 0831.17012 Feigin, Boris; Frenkel, Edward 21 1993 Trace formula and functionality: the beginnings of a program. (Formule des traces et fonctorialité: le début d’un programme.) Zbl 1267.11113 Frenkel, Edward; Langlands, Robert; Ngô, Bao Châu 21 2010 A family of representations of affine Lie algebras. Zbl 0657.17013 Feĭgin, B. L.; Frenkel, Edward V. 20 1988 \(D\)-modules on the affine Grassmannian and representations of affine Kac-Moody algebras. Zbl 1107.17013 Frenkel, Edward; Gaitsgory, Dennis 19 2004 Localization of \(\mathfrak g\)-modules on the affine Grassmannian. Zbl 1202.17009 Frenkel, Edward; Gaitsgory, Dennis 19 2009 Mirror symmetry in two steps: A–I–B. Zbl 1127.14035 Frenkel, Edward; Losev, Andrei 18 2007 D-modules on the affine flag variety and representations of affine Kac-Moody algebras. Zbl 1251.17012 Frenkel, Edward; Gaitsgory, Dennis 17 2009 Thermodynamic Bethe ansatz and dilogarithm identities. I. Zbl 1036.11514 Frenkel, Edward; Szenes, András 16 1995 Twisted modules over vertex algebras on algebraic curves. Zbl 1049.17024 Frenkel, Edward; Szczesny, Matthew 16 2004 Spectral curves, opers and integrable systems. Zbl 1113.14301 Ben-Zvi, David; Frenkel, Edward 16 2001 Langlands duality for finite-dimensional representations of quantum affine algebras. Zbl 1222.17014 Frenkel, Edward; Hernandez, David 15 2011 Representations of affine Kac-Moody algebras and bosonization. Zbl 0734.17011 Feĭgin, Boris L.; Frenkel, Edward V. 15 1990 Geometric realization of the Segal-Sugawara construction. Zbl 1170.17303 Ben-Zvi, David; Frenkel, Edward 15 2004 Quantum Langlands duality of representations of \(\mathcal{W}\)-algebras. Zbl 1475.17041 Arakawa, Tomoyuki; Frenkel, Edward 14 2019 An analytic version of the Langlands correspondence for complex curves. Zbl 1475.14021 Etingof, Pavel; Frenkel, Edward; Kazhdan, David 14 2021 Geometric realization of Whittaker functions and the Langlands conjecture. Zbl 1068.11501 Frenkel, E.; Gaitsgory, D.; Kazhdan, D.; Vilonen, K. 13 1998 Free field realizations in representation theory and conformal field theory. Zbl 0852.17023 Frenkel, Edward 13 1995 Weyl modules and opers without monodromy. Zbl 1231.17007 Frenkel, Edward; Gaitsgory, Dennis 13 2010 Folded quantum integrable models and deformed \(W\)-algebras. Zbl 1513.81077 Frenkel, Edward; Hernandez, David; Reshetikhin, Nicolai 13 2022 Local geometric Langlands correspondence: the spherical case. Zbl 1192.17012 Frenkel, Edward; Gaitsgory, Dennis 12 2009 Integrable hierarchies and Wakimoto modules. Zbl 0977.17020 Feigin, Boris; Frenkel, Edward 11 1999 Cohomology of the commutator subgroup of the braid group. Zbl 0675.20042 Frenkel’, Edward V. 11 1988 \(\mathcal W\)-algebras and Langlands-Drinfel’d correspondence. Zbl 1221.17023 Frenkel, Edward 11 1992 Geometric realizations of Wakimoto modules at the critical level. Zbl 1215.17016 Frenkel, Edward; Gaitsgory, Dennis 11 2008 Vertex algebras and algebraic curves. Zbl 0997.17015 Frenkel, Edward 10 2002 Gauge theory and Langlands duality. Zbl 1209.22009 Frenkel, Edward 10 2010 Bosonic ghost system and the Virasoro algebra. Zbl 1243.81086 Feigin, Boris; Frenkel, Edward 10 1990 Recent advances in the Langlands Program. Zbl 1070.11051 Frenkel, Edward 10 2004 The \(q\)-characters at roots of unity. Zbl 1020.17009 Frenkel, Edward; Mukhin, Evgeny 10 2002 Geometrization of trace formulas. Zbl 1319.22015 Frenkel, Edward; Ngô, Bao Châu 9 2011 Fusion and convolution: applications to affine Kac-Moody algebras at the critical level. Zbl 1146.17025 Frenkel, Edward; Gaitsgory, Dennis 9 2006 Self-extensions of Verma modules and differential forms on opers. Zbl 1162.17314 Frenkel, Edward; Teleman, Constantin 9 2006 Langlands duality for representations of quantum groups. Zbl 1219.17007 Frenkel, Edward; Hernandez, David 8 2011 Gerbal representations of double loop groups. Zbl 1280.22024 Frenkel, Edward; Zhu, Xinwen 8 2012 Love and math. The heart of hidden reality. Zbl 1319.00005 Frenkel, Edward 8 2013 Kac-Moody groups and integrability of soliton equations. Zbl 0829.58021 Feigin, Boris; Frenkel, Edward 7 1995 Gromov-Witten gauge theory. Zbl 1342.14111 Frenkel, Edward; Teleman, Constantin; Tolland, A. J. 7 2016 Equivalence of two approaches to integrable hierarchies of KdV type. Zbl 0873.35080 Enriquez, Benjamin; Frenkel, Edward 6 1997 Any flat bundle on a punctured disc has an oper structure. Zbl 1220.14013 Frenkel, Edward; Zhu, Xinwen 6 2010 Ramification of the geometric Langlands program. Zbl 1194.22022 Frenkel, Edward 6 2008 Chiral de Rham complex and orbifolds. Zbl 1184.14033 Frenkel, Edward; Szczesny, Matthew 5 2007 Analytic Langlands correspondence for \(PGL_2\) on \(\mathbb{P}^1\) with parabolic structures over local fields. Zbl 1495.14021 Etingof, Pavel; Frenkel, Edward; Kazhdan, David 5 2022 \(q\)-opers, \(QQ\)-systems, and Bethe Ansatz. Zbl 1534.82005 Frenkel, Edward; Koroteev, Peter; Sage, Daniel S.; Zeitlin, Anton M. 4 2024 Geometric interpretation of the Poisson structure in affine Toda field theories. Zbl 1047.37506 Enriquez, Benjamin; Frenkel, Edward 3 1998 Erratum: Semi-infinite Weil complex and the Virasoro algebra. Zbl 0753.17033 Feigin, Boris; Frenkel, Edward 3 1992 Crystal bases, dilogarithm identities, and torsion in algebraic \(K\)-theory. Zbl 0848.17019 Frenkel, Edward; Szenes, András 3 1995 Langlands program, trace formulas, and their geometrization. Zbl 1329.11121 Frenkel, Edward 3 2013 Is there an analytic theory of automorphic functions for complex algebraic curves? Zbl 1446.14005 Frenkel, Edward 3 2020 Dilogarithm identities, \(q\)-difference equations, and the Virasoro algebra. Zbl 0783.17012 Frenkel, Edward; Szenes, Andras 2 1993 Hecke operators and analytic Langlands correspondence for curves over local fields. Zbl 1539.11146 Etingof, Pavel; Frenkel, Edward; Kazhdan, David 2 2023 On strictly sparse subsets of a free group. Zbl 1126.20301 Averina, Ya. S.; Frenkel’, E. V. 2 2005 Geometric Langlands correspondence near opers. Zbl 1325.14023 Frenkel, Edward; Teleman, Constantin 2 2013 Five lectures on soliton equations. Zbl 0931.35147 Frenkel, Edward 2 1998 Amalgamated products of groups: measures of random normal forms. Zbl 1259.20032 Myasnikov, A. G.; Remeslennikov, V. N.; Frenkel, E. V. 2 2012 Extended Baxter relations and QQ-systems for quantum affine algebras. Zbl 07895057 Frenkel, Edward; Hernandez, David 2 2024 Love and math. The heart of hidden reality. Translated from the English by Thomas Filk. Original English edition published by Basic Books, New York, NY, USA, 2013. (Liebe und Mathematik. Im Herzen einer verborgenen Wirklichkeit.) Zbl 1329.00026 Frenkel, Edward 1 2014 A general framework and examples of the analytic Langlands correspondence. Zbl 07826260 Etingof, Pavel; Frenkel, Edward; Kazhdan, David 1 2024 On the endomorphisms of Weyl modules over affine Kac-Moody algebras at the critical level. Zbl 1169.81015 Feigin, Boris; Frenkel, Edward; Rybnikov, Leonid 1 2009 \(q\)-opers, \(QQ\)-systems, and Bethe Ansatz. Zbl 1534.82005 Frenkel, Edward; Koroteev, Peter; Sage, Daniel S.; Zeitlin, Anton M. 4 2024 Extended Baxter relations and QQ-systems for quantum affine algebras. Zbl 07895057 Frenkel, Edward; Hernandez, David 2 2024 A general framework and examples of the analytic Langlands correspondence. Zbl 07826260 Etingof, Pavel; Frenkel, Edward; Kazhdan, David 1 2024 Hecke operators and analytic Langlands correspondence for curves over local fields. Zbl 1539.11146 Etingof, Pavel; Frenkel, Edward; Kazhdan, David 2 2023 Folded quantum integrable models and deformed \(W\)-algebras. Zbl 1513.81077 Frenkel, Edward; Hernandez, David; Reshetikhin, Nicolai 13 2022 Analytic Langlands correspondence for \(PGL_2\) on \(\mathbb{P}^1\) with parabolic structures over local fields. Zbl 1495.14021 Etingof, Pavel; Frenkel, Edward; Kazhdan, David 5 2022 An analytic version of the Langlands correspondence for complex curves. Zbl 1475.14021 Etingof, Pavel; Frenkel, Edward; Kazhdan, David 14 2021 Quantum Langlands dualities of boundary conditions, \(D\)-modules, and conformal blocks. Zbl 1445.14024 Frenkel, Edward; Gaiotto, Davide 30 2020 Is there an analytic theory of automorphic functions for complex algebraic curves? Zbl 1446.14005 Frenkel, Edward 3 2020 Quantum Langlands duality of representations of \(\mathcal{W}\)-algebras. Zbl 1475.17041 Arakawa, Tomoyuki; Frenkel, Edward 14 2019 Quantum \(q\)-Langlands correspondence. Zbl 1422.22021 Aganagic, M.; Frenkel, E.; Okounkov, A. 49 2018 Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers. Zbl 1397.81060 Frenkel, Edward; Hernandez, David 38 2018 Surface operators and separation of variables. Zbl 1388.81811 Frenkel, Edward; Gukov, Sergei; Teschner, Jörg 34 2016 Gromov-Witten gauge theory. Zbl 1342.14111 Frenkel, Edward; Teleman, Constantin; Tolland, A. J. 7 2016 Baxter’s relations and spectra of quantum integrable models. Zbl 1332.82022 Frenkel, Edward; Hernandez, David 75 2015 Love and math. The heart of hidden reality. Translated from the English by Thomas Filk. Original English edition published by Basic Books, New York, NY, USA, 2013. (Liebe und Mathematik. Im Herzen einer verborgenen Wirklichkeit.) Zbl 1329.00026 Frenkel, Edward 1 2014 Love and math. The heart of hidden reality. Zbl 1319.00005 Frenkel, Edward 8 2013 Langlands program, trace formulas, and their geometrization. Zbl 1329.11121 Frenkel, Edward 3 2013 Geometric Langlands correspondence near opers. Zbl 1325.14023 Frenkel, Edward; Teleman, Constantin 2 2013 Gerbal representations of double loop groups. Zbl 1280.22024 Frenkel, Edward; Zhu, Xinwen 8 2012 Amalgamated products of groups: measures of random normal forms. Zbl 1259.20032 Myasnikov, A. G.; Remeslennikov, V. N.; Frenkel, E. V. 2 2012 Quantization of soliton systems and Langlands duality. Zbl 1245.81062 Feigin, Boris; Frenkel, Edward 49 2011 Instantons beyond topological theory. I. Zbl 1230.81050 Frenkel, E.; Losev, A.; Nekrasov, N. 30 2011 Langlands duality for finite-dimensional representations of quantum affine algebras. Zbl 1222.17014 Frenkel, Edward; Hernandez, David 15 2011 Geometrization of trace formulas. Zbl 1319.22015 Frenkel, Edward; Ngô, Bao Châu 9 2011 Langlands duality for representations of quantum groups. Zbl 1219.17007 Frenkel, Edward; Hernandez, David 8 2011 Gaudin models with irregular singularities. Zbl 1186.81065 Feigin, B.; Frenkel, E.; Toledano Laredo, V. 52 2010 Opers with irregular singularity and spectra of the shift of argument subalgebra. Zbl 1226.22017 Feigin, Boris; Frenkel, Edward; Rybnikov, Leonid 33 2010 Soliton equations, vertex operators, and simple singularities. Zbl 1203.37108 Frenkel, Edward; Givental, Alexander; Milanov, Todor 22 2010 Trace formula and functionality: the beginnings of a program. (Formule des traces et fonctorialité: le début d’un programme.) Zbl 1267.11113 Frenkel, Edward; Langlands, Robert; Ngô, Bao Châu 21 2010 Weyl modules and opers without monodromy. Zbl 1231.17007 Frenkel, Edward; Gaitsgory, Dennis 13 2010 Gauge theory and Langlands duality. Zbl 1209.22009 Frenkel, Edward 10 2010 Any flat bundle on a punctured disc has an oper structure. Zbl 1220.14013 Frenkel, Edward; Zhu, Xinwen 6 2010 A rigid irregular connection on the projective line. Zbl 1209.14017 Frenkel, Edward; Gross, Benedict 31 2009 Localization of \(\mathfrak g\)-modules on the affine Grassmannian. Zbl 1202.17009 Frenkel, Edward; Gaitsgory, Dennis 19 2009 D-modules on the affine flag variety and representations of affine Kac-Moody algebras. Zbl 1251.17012 Frenkel, Edward; Gaitsgory, Dennis 17 2009 Local geometric Langlands correspondence: the spherical case. Zbl 1192.17012 Frenkel, Edward; Gaitsgory, Dennis 12 2009 On the endomorphisms of Weyl modules over affine Kac-Moody algebras at the critical level. Zbl 1169.81015 Feigin, Boris; Frenkel, Edward; Rybnikov, Leonid 1 2009 Geometric endoscopy and mirror symmetry. Zbl 1223.14014 Frenkel, Edward; Witten, Edward 24 2008 Geometric realizations of Wakimoto modules at the critical level. Zbl 1215.17016 Frenkel, Edward; Gaitsgory, Dennis 11 2008 Ramification of the geometric Langlands program. Zbl 1194.22022 Frenkel, Edward 6 2008 Langlands correspondence for loop groups. Zbl 1133.22009 Frenkel, Edward 110 2007 Lectures on the Langlands program and conformal field theory. Zbl 1196.11091 Frenkel, Edward 46 2007 Mirror symmetry in two steps: A–I–B. Zbl 1127.14035 Frenkel, Edward; Losev, Andrei 18 2007 Chiral de Rham complex and orbifolds. Zbl 1184.14033 Frenkel, Edward; Szczesny, Matthew 5 2007 Local geometric Langlands correspondence and affine Kac-Moody algebras. Zbl 1184.17011 Frenkel, Edward; Gaitsgory, Dennis 45 2006 Fusion and convolution: applications to affine Kac-Moody algebras at the critical level. Zbl 1146.17025 Frenkel, Edward; Gaitsgory, Dennis 9 2006 Self-extensions of Verma modules and differential forms on opers. Zbl 1162.17314 Frenkel, Edward; Teleman, Constantin 9 2006 Wakimoto modules, opers and the center at the critical level. Zbl 1129.17014 Frenkel, Edward 74 2005 Gaudin model and opers. Zbl 1132.17305 Frenkel, Edward 30 2005 On strictly sparse subsets of a free group. Zbl 1126.20301 Averina, Ya. S.; Frenkel’, E. V. 2 2005 Vertex algebras and algebraic curves. 2nd revised and expanded ed. Zbl 1106.17035 Frenkel, Edward; Ben-Zvi, David 242 2004 Opers on the projective line, flag manifolds and Bethe Ansatz. Zbl 1087.82008 Frenkel, Edward 30 2004 \(D\)-modules on the affine Grassmannian and representations of affine Kac-Moody algebras. Zbl 1107.17013 Frenkel, Edward; Gaitsgory, Dennis 19 2004 Twisted modules over vertex algebras on algebraic curves. Zbl 1049.17024 Frenkel, Edward; Szczesny, Matthew 16 2004 Geometric realization of the Segal-Sugawara construction. Zbl 1170.17303 Ben-Zvi, David; Frenkel, Edward 15 2004 Recent advances in the Langlands Program. Zbl 1070.11051 Frenkel, Edward 10 2004 The Hopf algebra \(\text{Rep\,} U_q \widehat{\mathfrak g\mathfrak l}_\infty\). Zbl 1034.17009 Frenkel, E.; Mukhin, E. 36 2002 On the geometric Langlands conjecture. Zbl 1071.11039 Frenkel, E.; Gaitsgory, D.; Vilonen, K. 24 2002 Vertex algebras and algebraic curves. Zbl 0997.17015 Frenkel, Edward 10 2002 The \(q\)-characters at roots of unity. Zbl 1020.17009 Frenkel, Edward; Mukhin, Evgeny 10 2002 Vertex algebras and algebraic curves. Zbl 0981.17022 Frenkel, Edward; Ben-Zvi, David 134 2001 Combinatorics of \(q\)-characters of finite-dimensional representations of quantum affine algebras. Zbl 1051.17013 Frenkel, Edward; Mukhin, Evgeny 108 2001 Whittaker patterns in the geometry of moduli spaces of bundles on curves. Zbl 1070.11050 Frenkel, E.; Gaitsgory, D.; Vilonen, K. 30 2001 Spectral curves, opers and integrable systems. Zbl 1113.14301 Ben-Zvi, David; Frenkel, Edward 16 2001 The \(q\)-characters of representations of quantum affine algebras and deformations of \(W\)-algebras. Zbl 0973.17015 Frenkel, Edward; Reshetikhin, Nicolai 187 1999 Integrable hierarchies and Wakimoto modules. Zbl 0977.17020 Feigin, Boris; Frenkel, Edward 11 1999 Deformations of \(W\)-algebras associated to simple Lie algebras. Zbl 0939.17011 Frenkel, Edward; Reshetikhin, Nicolai 61 1998 Drinfeld-Sokolov reduction for difference operators and deformations of \({\mathcal W}\)-algebras. I: The case of Virasoro algebra. Zbl 0916.17020 Frenkel, E.; Reshetikhin, N.; Semenov-Tian-Shansky, M. A. 26 1998 Geometric realization of Whittaker functions and the Langlands conjecture. Zbl 1068.11501 Frenkel, E.; Gaitsgory, D.; Kazhdan, D.; Vilonen, K. 13 1998 Geometric interpretation of the Poisson structure in affine Toda field theories. Zbl 1047.37506 Enriquez, Benjamin; Frenkel, Edward 3 1998 Five lectures on soliton equations. Zbl 0931.35147 Frenkel, Edward 2 1998 Equivalence of two approaches to integrable hierarchies of KdV type. Zbl 0873.35080 Enriquez, Benjamin; Frenkel, Edward 6 1997 Quantum affine algebras and deformations of the Virasoro and \({\mathcal W}\)-algebras. Zbl 0869.17014 Frenkel, Edward; Reshetikhin, Nikolai 84 1996 Quantum \({\mathcal W}\)-algebras and elliptic algebras. Zbl 0871.17007 Feigin, Boris; Frenkel, Edward 67 1996 Integrals of motion and quantum groups. Zbl 0885.58034 Feigin, Boris; Frenkel, Edward 49 1996 Deformations of the KdV hierarchy and related soliton equations. Zbl 0860.17033 Frenkel, Edward 30 1996 \({\mathcal W}_{1+\infty}\) and \({\mathcal W}(gl_ N)\) with central charge \(N\). Zbl 0838.17028 Frenkel, Edward; Kac, Victor; Radul, Andrey; Wang, Weiqiang 114 1995 Affine algebras, Langlands duality and Bethe ansatz. Zbl 1052.17504 Frenkel, Edward 34 1995 Thermodynamic Bethe ansatz and dilogarithm identities. I. Zbl 1036.11514 Frenkel, Edward; Szenes, András 16 1995 Free field realizations in representation theory and conformal field theory. Zbl 0852.17023 Frenkel, Edward 13 1995 Kac-Moody groups and integrability of soliton equations. Zbl 0829.58021 Feigin, Boris; Frenkel, Edward 7 1995 Crystal bases, dilogarithm identities, and torsion in algebraic \(K\)-theory. Zbl 0848.17019 Frenkel, Edward; Szenes, András 3 1995 Gaudin model, Bethe ansatz and critical level. Zbl 0812.35103 Feigin, Boris; Frenkel, Edward; Reshetikhin, Nikolai 131 1994 Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities. Zbl 0831.17012 Feigin, Boris; Frenkel, Edward 21 1993 Dilogarithm identities, \(q\)-difference equations, and the Virasoro algebra. Zbl 0783.17012 Frenkel, Edward; Szenes, Andras 2 1993 Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras. Zbl 0925.17022 Feigin, Boris; Frenkel, Edward 139 1992 Characters and fusion rules for \(W\)-algebras via quantized Drinfeld- Sokolov reduction. Zbl 0768.17008 Frenkel, Edward; Kac, Victor; Wakimoto, Minoru 101 1992 \(\mathcal W\)-algebras and Langlands-Drinfel’d correspondence. Zbl 1221.17023 Frenkel, Edward 11 1992 Erratum: Semi-infinite Weil complex and the Virasoro algebra. Zbl 0753.17033 Feigin, Boris; Frenkel, Edward 3 1992 Duality in \(W\)-algebras. Zbl 0790.17013 Feigin, Boris; Frenkel, Edward 27 1991 Semi-infinite Weil complex and the Virasoro algebra. Zbl 0726.17035 Feigin, Boris; Frenkel, Edward 23 1991 Quantization of the Drinfel’d-Sokolov reduction. Zbl 1242.17023 Feigin, Boris; Frenkel, Edward 138 1990 Affine Kac-Moody algebras and semi-infinite flag manifolds. Zbl 0722.17019 Feigin, Boris L.; Frenkel, Edward V. 89 1990 Representations of affine Kac-Moody algebras, bosonization and resolutions. Zbl 0711.17012 Feigin, Boris L.; Frenkel, Edward V. 56 1990 Representations of affine Kac-Moody algebras and bosonization. Zbl 0734.17011 Feĭgin, Boris L.; Frenkel, Edward V. 15 1990 Bosonic ghost system and the Virasoro algebra. Zbl 1243.81086 Feigin, Boris; Frenkel, Edward 10 1990 A family of representations of affine Lie algebras. Zbl 0668.17015 Feigin, B. L.; Frenkel’, Edward V. 27 1988 A family of representations of affine Lie algebras. Zbl 0657.17013 Feĭgin, B. L.; Frenkel, Edward V. 20 1988 Cohomology of the commutator subgroup of the braid group. Zbl 0675.20042 Frenkel’, Edward V. 11 1988 all cited Publications top 5 cited Publications all top 5 Cited by 1,514 Authors 47 Feĭgin, Boris L’vovich 43 Creutzig, Thomas 43 Frenkel, Edward V. 34 Arakawa, Tomoyuki 34 Mukhin, Evgeny 32 Linshaw, Andrew Ross 28 Adamović, Dražen 23 Molev, Alexander I. 21 Kac, Victor 20 Hernandez, David 20 Milas, Antun 20 Oh, Se-jin 19 Li, Haisheng 17 Young, Charles A. S. 16 Futorny, Vyacheslav M. 16 Jing, Naihuan 16 Zeitlin, Anton M. 14 Awata, Hidetoshi 14 Cox, Ben Lewis 14 Gaitsgory, Dennis 14 Jimbo, Michio 14 Nekrasov, Nikita Alexandrovich 14 Ragoucy, Eric 14 Vicedo, Benoît 13 Gaiotto, Davide 13 Kashiwara, Masaki 13 Varchenko, Alexander Nikolaevich 13 Zhang, Yaozhong 12 Morozov, Alexei Yurievich 12 Ridout, David 12 Shiraishi, Jun’ichi 11 Ding, Xiangmao 11 Genra, Naoki 11 Lacroix, Sylvain 11 Lukyanov, Sergei L. 11 Rasmussen, Jorgen 11 Yang, Wenli 10 Chari, Vyjayanthi 10 Feigin, Evgeny 10 Heluani, Reimundo 10 Kanno, Hiroaki 10 Kimura, Taro 10 Mironov, Andrei D. 10 Rybnikov, Leonid Grigor’evich 10 Zabzine, Maxim 10 Zenkevich, Yegor 9 Biswas, Indranil 9 Frappat, Luc 9 Kim, Myungho 9 Moreau, Anne 9 Wakimoto, Minoru 9 Wang, Weiqiang 9 Yakimova, Oksana S. 8 Bazhanov, Vladimir V. 8 Etingof, Pavel Il’ich 8 Gukov, Sergei 8 Kamgarpour, Masoud 8 Kanade, Shashank 8 Kojima, Takeo 8 Koroteev, Peter 8 Kožić, Slaven 8 Liu, Siqi 8 Manojlović, Nenad 8 Moura, Adriano A. 8 Nieri, Fabrizio 8 Park, Euiyong 8 Pestun, Vasily 8 Raskin, Sam 8 Runkel, Ingo 8 Teschner, Jörg 8 Tsuboi, Zengo 8 van Ekeren, Jethro 8 Zhang, Huafeng 8 Zhang, Youjin 8 Zuevsky, Alexander 7 Anguelova, Iana I. 7 Avan, Jean 7 Bakalov, Bojko 7 Bourgine, Jean-Emile 7 De Sole, Alberto 7 Dubrovin, Boris Anatol’evich 7 Duncan, John F. R. 7 Frenkel, Igor B. 7 Fuchs, Jürgen 7 Ito, Katsushi 7 Jiang, Cuipo 7 Kedem, Rinat 7 Losev, Andrei S. 7 Malikov, Fyodor 7 Masoero, Davide 7 Miwa, Tetsuji 7 Nakajima, Hiraku 7 Nakanishi, Tomoki 7 Odake, Satoru 7 Procházka, Tomáš 7 Razumov, Alexander V. 7 Sage, Daniel S. 7 Semikhatov, Alexei M. 7 Su, Yucai 7 Zhu, Xinwen ...and 1,414 more Authors all top 5 Cited in 183 Serials 184 Communications in Mathematical Physics 165 Journal of High Energy Physics 117 Advances in Mathematics 110 Nuclear Physics. B 93 Letters in Mathematical Physics 86 Journal of Algebra 69 Journal of Mathematical Physics 43 Selecta Mathematica. New Series 38 Journal of Geometry and Physics 31 Journal of Physics A: Mathematical and Theoretical 28 Theoretical and Mathematical Physics 27 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 26 Duke Mathematical Journal 26 Transactions of the American Mathematical Society 26 Transformation Groups 22 Mathematische Zeitschrift 22 Representation Theory 21 Communications in Contemporary Mathematics 20 Compositio Mathematica 19 Algebras and Representation Theory 16 Journal of Pure and Applied Algebra 15 Inventiones Mathematicae 13 Communications in Algebra 13 Proceedings of the London Mathematical Society. Third Series 13 Annales Henri Poincaré 12 Physics Letters. B 12 Reviews in Mathematical Physics 12 Journal of the Institute of Mathematics of Jussieu 11 Journal für die Reine und Angewandte Mathematik 11 Journal of the American Mathematical Society 11 Bulletin of the American Mathematical Society. New Series 11 Annals of Mathematics. 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Série VI 5 Journal of Algebraic Geometry 5 Forum of Mathematics, Sigma 4 International Journal of Modern Physics B 4 Publications Mathématiques 4 Transactions of the Moscow Mathematical Society 4 Annals of Physics 4 Journal of Algebraic Combinatorics 4 The Ramanujan Journal 4 Algebra & Number Theory 4 European Journal of Mathematics 4 Journal de l’École Polytechnique – Mathématiques 3 Modern Physics Letters A 3 Reports on Mathematical Physics 3 The Mathematical Intelligencer 3 Applied Mathematics and Computation 3 Canadian Journal of Mathematics 3 Journal of Functional Analysis 3 Journal of Number Theory 3 Nagoya Mathematical Journal 3 Chinese Annals of Mathematics. Series B 3 Acta Applicandae Mathematicae 3 Journal of Mathematical Sciences (New York) 3 Geometry & Topology 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Central European Journal of Mathematics 3 Journal of Statistical Mechanics: Theory and Experiment 3 Frontiers of Mathematics in China 3 Communications in Theoretical Physics 3 Advances in Mathematical Physics 3 Kyoto Journal of Mathematics 3 Annales Mathématiques du Québec 2 Nonlinearity 2 Bulletin of the London Mathematical Society 2 Journal of Combinatorial Theory. Series A 2 Journal of Differential Geometry 2 Journal of the Indian Institute of Science 2 Journal of the Mathematical Society of Japan 2 Michigan Mathematical Journal 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Tôhoku Mathematical Journal. Second Series 2 Forum Mathematicum 2 Geometric and Functional Analysis. GAFA 2 Indagationes Mathematicae. New Series 2 Journal of Knot Theory and its Ramifications 2 Nuclear Physics. B. Proceedings Supplements 2 Applied Categorical Structures 2 Algebra Colloquium 2 Bulletin des Sciences Mathématiques ...and 83 more Serials all top 5 Cited in 54 Fields 1,030 Nonassociative rings and algebras (17-XX) 865 Quantum theory (81-XX) 381 Algebraic geometry (14-XX) 147 Associative rings and algebras (16-XX) 145 Dynamical systems and ergodic theory (37-XX) 144 Statistical mechanics, structure of matter (82-XX) 129 Group theory and generalizations (20-XX) 128 Number theory (11-XX) 127 Topological groups, Lie groups (22-XX) 87 Category theory; homological algebra (18-XX) 76 Differential geometry (53-XX) 68 Partial differential equations (35-XX) 61 Relativity and gravitational theory (83-XX) 60 Commutative algebra (13-XX) 59 Combinatorics (05-XX) 50 Global analysis, analysis on manifolds (58-XX) 48 Several complex variables and analytic spaces (32-XX) 47 Special functions (33-XX) 39 Manifolds and cell complexes (57-XX) 27 Ordinary differential equations (34-XX) 26 \(K\)-theory (19-XX) 23 Mechanics of particles and systems (70-XX) 19 Functional analysis (46-XX) 18 Algebraic topology (55-XX) 16 Functions of a complex variable (30-XX) 16 Difference and functional equations (39-XX) 15 General and overarching topics; collections (00-XX) 11 Probability theory and stochastic processes (60-XX) 9 Statistics (62-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 8 Operator theory (47-XX) 6 History and biography (01-XX) 6 Field theory and polynomials (12-XX) 6 Abstract harmonic analysis (43-XX) 6 Geometry (51-XX) 4 General algebraic systems (08-XX) 4 Numerical analysis (65-XX) 3 Convex and discrete geometry (52-XX) 3 Computer science (68-XX) 3 Fluid mechanics (76-XX) 3 Information and communication theory, circuits (94-XX) 2 Potential theory (31-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 2 Optics, electromagnetic theory (78-XX) 2 Mathematics education (97-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Measure and integration (28-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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