@incollection{AST_2010__332__369_0, author = {Frenkel, Edward}, title = {Gauge theory and {Langlands} duality}, booktitle = {S\'eminaire Bourbaki : volume 2008/2009 expos\'es 997-1011 - Avec table par noms d'auteurs de 1848/49 \`a 2008/09}, series = {Ast\'erisque}, note = {talk:1010}, pages = {369--403}, publisher = {Soci\'et\'e math\'ematique de France}, number = {332}, year = {2010}, mrnumber = {2648685}, zbl = {1209.22009}, language = {en}, url = {http://www.numdam.org/item/AST_2010__332__369_0/} }
TY - CHAP AU - Frenkel, Edward TI - Gauge theory and Langlands duality BT - Séminaire Bourbaki : volume 2008/2009 exposés 997-1011 - Avec table par noms d'auteurs de 1848/49 à 2008/09 AU - Collectif T3 - Astérisque N1 - talk:1010 PY - 2010 SP - 369 EP - 403 IS - 332 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_2010__332__369_0/ LA - en ID - AST_2010__332__369_0 ER -
%0 Book Section %A Frenkel, Edward %T Gauge theory and Langlands duality %B Séminaire Bourbaki : volume 2008/2009 exposés 997-1011 - Avec table par noms d'auteurs de 1848/49 à 2008/09 %A Collectif %S Astérisque %Z talk:1010 %D 2010 %P 369-403 %N 332 %I Société mathématique de France %U http://www.numdam.org/item/AST_2010__332__369_0/ %G en %F AST_2010__332__369_0
Frenkel, Edward. Gauge theory and Langlands duality, dans Séminaire Bourbaki : volume 2008/2009 exposés 997-1011 - Avec table par noms d'auteurs de 1848/49 à 2008/09, Astérisque, no. 332 (2010), Exposé no. 1010, 35 p. http://www.numdam.org/item/AST_2010__332__369_0/
[1] Moduli of connections with a small parameter on a curve", preprint arXiv:mathAG/0409373.
- "[2] Unipotent automorphic representations: conjectures", Astérisque 171-172(1989), p. 13-71. | Numdam | MR | Zbl
- "[3] Quantization of Hitchin's integrable system and Hecke eigensheaves", preprint http://www.math.uchicago.edu/~mitya/langlands/hitchin/BD-hitchin.pdf.
& - "[4] Topological reduction of to -models", Nuclear Phys. B 448 (1995), p. 166-186. | DOI | MR | Zbl
, , & - "[5] Flat -bundles with canonical metrics", J. Differential Geom. 28 (1988), p. 361-382. | DOI | MR | Zbl
- "[6] Quantum fields and strings : A course for mathematicians, Vol. I and II, Amer. Math. Soc, Institute for Advanced Study, 1999.
-[7] Langlands duality for Hitchin systems", preprint arXiv:math. AG/0604617. | DOI | MR | Zbl
& - "[8] Langlands' conjecture for over functional fields", in Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, 1980, p. 565-574. | MR | Zbl
- "[9] Two-dimensional -adic representations of the fundamental group of a curve over a finite field and automorphic forms on ", Amer. J. Math. 105 (1983), p. 85-114. | DOI | MR | Zbl
, "[10] Moduli varieties of -sheaves", Funct. Anal Appl. 21 (1987), p. 107-122. | DOI | MR | Zbl
, "[11] The proof of Petersson's conjecture for over a global field of characteristic ", Funct. Anal. Appl. 22 (1988), p. 28-43. | DOI | MR | Zbl
, "[12] Quantization condition for Hooft monopoles in compact simple Lie groups", Phys. Rev D 14 (1976), p. 2728-2731. | DOI | MR
& - "[13] Recent advances in the Langlands program", Bull. Amer. Math. Soc. (N.S.) 41 (2004), p. 151-184. | DOI | MR | Zbl
- "[14] Langlands correspondence for loop groups, Cambridge Studies in Advanced Math., vol. 103, Cambridge Univ. Press, 2007. | MR | Zbl
,[15] Lectures on the Langlands program and conformai field theory", in Frontiers in number theory, physics, and geometry. II, Springer, 2007, p. 387-533. | DOI | MR | Zbl
, "[16] Local geometric Langlands correspondence and affine Kac-Moody algebras", in Algebraic geometry and number theory, Progr. Math., vol. 253, Birkhäuser, 2006, p. 69-260. | DOI | MR | Zbl
& - "[17] On the geometric Langlands conjecture", J. Amer. Math. Soc. 15 (2002), p. 367-417. | DOI | MR | Zbl
, & - "[18] -duality of branes and geometric Langlands correspondence", to appear.
& - "[19] Geometric endoscopy and mirror symmetry", Commun. Number Theory Phys. 2 (2008), p. 113-283. | DOI | MR | Zbl
& - "[20] Supersymmetric boundary conditions in super Yang-Mills theory", J. Stat. Phys. 135 (2009), p. 789-855. | DOI | MR | Zbl
& - "[21] -duality of boundary conditions in super Yang-Mills theory", preprint arXiv:0807.3720. | DOI | MR | Zbl
& , "[22] On a vanishing conjecture appearing in the geometric Langlands correspondence", Ann. of Math. 160 (2004), p. 617-682. | DOI | MR | Zbl
- "[23] An elementary introduction to the Langlands program", Bull. Amer. Math. Soc. (N.S.) 10 (1984), p. 177-219. | DOI | MR | Zbl
- "[24] Homological algebra, Encyclopaedia of Math. Sciences, vol. 38, Springer, 1994. | MR | Zbl
& -[25] Gauge theories and magnetic charge", Nuclear Phys. B 125 (1977), p. 1-28. | DOI | MR
, & - "[26] Gauge theory, ramification, and the geometric Langlands program", in Current developments in mathematics, 2006, Int. Press, Somerville, MA, 2008, p. 35-180. | MR | Zbl
& - "[27] Rigid surface operators", preprint arXiv:0804.1561. | DOI | MR | Zbl
& , "[28] Reducing duality to duality", Phys. Rev. D 52 (1995), p. 7161-7167. | DOI | MR
, & - "[29] Mirror symmetry, Langlands duality, and the Hitchin system", Invent. Math. 153 (2003), p. 197-229. | DOI | MR | Zbl
& - "[30] The self-duality equations on a Riemann surface", Proc. London Math. Soc. 55 (1987), p. 59-126. | DOI | MR | Zbl
- "[31] Stable bundles and integrable systems", Duke Math. J. 54 (1987), p. 91-114. | DOI | MR | Zbl
, "[32] Langlands duality and spectral curves", Q. J. Math. 58 (2007), p. 319-344. | DOI | MR | Zbl
, "[33] A note on quantum geometric Langlands duality, gauge theory, and quantization of the moduli space of flat connections", preprint arXiv:0811.3264.
- "[34] Electric-magnetic duality and the geometric Langlands program", Commun. Number Theory Phys. 1 (2007), p. 1-236. | DOI | MR | Zbl
& - "[35] Sheaves on manifolds, Grund. Math. Wiss., vol. 292, Springer, 1990. | MR | Zbl
& -[36] A 1940 letter of André Weil on analogy in mathematics", Notices Amer. Math. Soc. 52 (2005), p. 334-341. | MR | Zbl
- "[37] Chtoucas de Drinfeld et correspondance de Langlands", Invent. Math. 147 (2002), p. 1-241. | DOI | MR | Zbl
- "[38] Quelques calculs reliés à la correspondance de Langlands géométrique pour ", preprint http://people.math.jussieu.fr/~vlafforg/geom.pdf.
, "[39] Problems in the theory of automorphic forms", in Lectures in modern analysis and applications, III, Lecture Notes in Math., vol. 170, Springer, 1970, p. 18-61. | MR | Zbl
- "[40] Correspondance de Langlands géométrique pour les corps de fonctions", Duke Math. J. 54 (1987), p. 309-359. | MR | Zbl
- "[41] Transformation de Fourier généralisée", preprint arXiv:alggeom/9603004. | Numdam | MR | Zbl
, "[42] Geometric Waldspurger periods", Compos. Math. 144 (2008), p. 377-438. | DOI | MR | Zbl
- "[43] Geometric theta-lifting for the dual pair ", preprint arXiv:0802.0457. | Numdam | MR | Zbl
, "[44], "Geometric theta-lifting for the dual pair ", preprint arXiv:math/0701170.
[45] Geometric Langlands duality and representations of algebraic groups over commutative rings", Ann. of Math. 166 (2007), p. 95-143. | DOI | MR | Zbl
& - "[46] Magnetic monopoles as gauge particles ?", Phys. Lett. B 72 (1977), p. 117-120. | DOI
& - "[47] Microlocal branes are constructible sheaves", preprint arXiv:math/0612399. | DOI | MR | Zbl
- "[48] Constructible sheaves and the Fukaya category", J. Amer. Math. Soc. 22 (2009), p. 233-286. | DOI | MR | Zbl
& - "[49] Le lemme fondamental pour les algèbres de Lie", preprint arXiv:0801.0446. | Numdam | MR | Zbl
- "[50] Topological charges for supersymmetric gauge theories and monopoles of Spin 1", Phys. Lett. B 83 (1979), 321-326. | DOI
- "[51] Connections on the total Picard sheaf and the hierarchy", Acta Appl. Math. 42 (1996), p. 297-308. | DOI | MR | Zbl
- "[52] Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization", J. Amer. Math. Soc. 1 (1988), p. 867-918. | DOI | MR | Zbl
- "[53] Harmonic bundles on noncompact curves", J. Amer. Math. Soc.. 3 (1990), p. 713-770. | DOI | MR | Zbl
, "[54] Mirror symmetry is -duality", Nuclear Phys. B 479 (1996), p. 243-259. | DOI | MR | Zbl
, & - "[55] A strong coupling test of -duality", Nuclear Phys. B 431 (1994), p. 3-77. | DOI | Zbl
& - "[56] Topological quantum field theory", Comm. Math. Phys. 117 (1988), p. 353-386. | DOI | Zbl
- "[57] Mirror manifolds and topological field theory", in Essays on mirror manifolds, Int. Press, Hong Kong, 1992, p. 120-158. | Zbl
, "[58] Gauge theory and wild ramification", Anal. Appl. (Singap.) 6 (2008), p. 429-501. | DOI | Zbl
, "[59] Geometric Langlands and the equations of Nahm and Bogomolny", to appear. | DOI | Zbl
, "[60] Geometric Langlands from six dimensions", preprint arXiv:0905.2720. | DOI | Zbl
, "[61] Mirror symmetry, Hitchin's equations, and Langlands duality", preprint arXiv:0802.0999. | DOI | Zbl
, "