Lecture Notes on Representation theory and Geometric Langlands
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Lecture Notes from the Special Year on New Connections of
Representation Theory to Algebraic Geometry and Physics.
Institute for Advanced Study, 2007-8.
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Notes from Vienna workshop on Geometric Langlands and Physics, January 2007
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Notes from
Gottingen Winterschule
on Geometric Langlands, January 2007
- Alexander Beilinson:
Quantization of Hitchin Hamiltonians and Hecke Eigensheaves (MIT,
Kac Seminar, 10/95)
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Chiral Algebras and Hecke Eigensheaves (Brandeis, Colloquium, 4/96)
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Chiral Hecke Algebras (IAS, Langlands birthday conference, 10/96)
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Hecke Eigensheaf Property
11pp. (IAS, Langlands
seminar, 4/97 - sequel to Drinfeld lectures on Quantization)
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Introduction to Geometric Langlands
21pp. (U. of Chicago Geometric Langlands seminar, 10/99)
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Nearby Hecke Functors and Kac-Moody Modules
4pp. (U. of Chicago Geometric Langlands seminar, 6/00)
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Triangulated categories 16pp. (U. of Chicago Geometric Langlands
seminar, 11/01)
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Differential operators on ind-schemes
12pp. (U. of Chicago Geometric Langlands seminar, 11/03)
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On the Langlands Correspondence in the de Rham Setting, I and
II
(MSRI Geometric Langlands
conference, 3/02)
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Topological Epsilon Factors
(Luminy Langlands Program meeting, 6/06)
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Connections on the punctured disc (Evanston Noncommutative Geometry
Conference, 5/07)
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Factorization and the determination of periods (Gauge Theory and Representation
Theory, IAS, 11/07)
- Joseph Bernstein:
Nearby and Vanishing Cycles (Lecture from a graduate course, UC
Berkeley, 1/02)
- Roman Bezrukavnikov:
Sheaves on Affine Flags and Modular Representations of Langlands Dual
Lie Algebra
(MSRI Geometric Langlands conference, 3/02)
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Geometric Langlands and Positive Characteristic (Luminy Langlands
Program meeting, 6/06)
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Local Geometric Langlands Correspondence (Vienna Geometric Langlands and Physics meeting,
1/07)
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Stability Conditions
(IAS Spring Term 2008)
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Stability Conditions II
(IAS Spring Term 2008)
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Representations of Rational Cherednik Algebras and Miracles of Science
(IAS Spring Term 2008)
- Olivier Biquard:
Wild nonabelian Hodge theory (Vienna Geometric Langlands and Physics meeting,
1/07)
- Mitya Boyarchenko:
Character Sheaves and the Orbit Method
(Luminy Langlands Program meeting, 6/06. )
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Characters of Unipotent Groups over Finite Fields
(UT Austin Geometry Seminar, 8/07. )
- Alexander Braverman:
The double affine Grassmannian via instantons on ALE spaces (IAS Conference on Representation Theory and Gauge Theory, November 2007)
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Satake isomorphism for loop groups
(IAS Spring Term 2008)
- Vladimir Drinfeld:
Introduction to Eisenstein Series, Parts I-III
20pp. (U. of Chicago Geometric Langlands
seminar, 11/99)
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Quantization of Hitchin's Hamiltonians and Opers, Parts I-IV
17pp. (IAS, Langlands
seminar, 3/97)
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Lectures on DG Categories
23pp. (U. of Chicago Geometric Langlands
seminar, 10/02)
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Some Geometric Langlands Problems
19pp. (U. of Chicago, DARPA Langlands
seminar, 10/03)
- Misha Finkelberg
Uhlenbeck spaces for A^2 and affine Lie algebras. 4pp. (AMS
meeting, Northwestern U., 10/04)
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Toda lattice and quasimaps.
5pp.
(U. of Chicago, DARPA Langlands Seminar 10/04)
- Edward Frenkel:
Introduction to Geometric Langlands
(U.C. Davis AMS Meeting, Plenary Lecture, 4/98)
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Geometric Langlands and Affine Kac-Moody Algebras I-II 7pp.
(Northwestern University, 4/02)
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Critical Level Representations and Local Langlands I-II 13pp. (U. of
Chicago, DARPA Langlands meetings, 11/03. With comments by Drinfeld
and Bezrukavnikov.)
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Ramifications of the Geometric Langlands Program (Vienna Geometric Langlands and Physics workshop, 1/07)
- Ramified Geometric Langlands I
(Vienna Geometric Langlands and Physics workshop, 1/07)
- Ramified Geometric Langlands II
(Vienna Geometric Langlands and Physics workshop, 1/07)
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Geometric Endoscopy and Mirror Symmetry
(Gauge Theory and Representation
Theory, IAS, 11/07)
- Dennis Gaitsgory:
Geometric Eisenstein Series 6pp.
(U. of Chicago Geometric Langlands Seminar, 12/99)
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Local Geometric Langlands 7pp.
(U. of Chicago, DARPA Langlands Seminar 11/03)
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Two-dimensional Geometric Langlands? 3pp.
(U. of Chicago, DARPA Langlands Seminar 10/04)
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de Jong's Conjecture 4pp.
(AMS meeting, Northwestern U., 10/04)
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Lecture Series on Beilinson-Bernstein Localization for Loop Groups 39pp.
(U. of Chicago Geometric Langlands Seminar 10/04)
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Local Geometric Langlands and localization of Kac-Moody modules (Gauge Theory and Representation
Theory, IAS, 11/07)
- Victor Ginzburg:
Harish-Chandra homomorphism and Calogero-Moser Spaces I-II
11pp.
(Geometric Langlands Seminar, U. of Chicago, 10/00)
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Symplectic Reflection Algebras I-IV
21pp.
(Geometric Langlands Seminar, U. of Chicago, 11/00)
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Vanishing Cycles for D-Modules 13pp.
(Lectures from a graduate course, U. of Chicago, Spring 2001)
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Calabi-Yau Algebras and Noncommutative Geometry (Gauge Theory and Representation
Theory, IAS, 11/07)
- Ian Grojnowski :
Satake for double loop groups.
7pp.
(U. of Chicago, DARPA Langlands Seminar 10/04)
- Sergei Gukov:
Gauge theory and tamely ramified Geometric Langlands I
(Vienna Geometric Langlands and Physics workshop, 1/07)
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Tamely ramified Langlands II
(Vienna Geometric Langlands and Physics workshop, 1/07)
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Tamely ramified Langlands III
(Vienna Geometric Langlands and Physics workshop, 1/07)
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D-branes and Representation Theory
(Gauge Theory and Representation
Theory, IAS, 11/07)
- Misha Kapranov:
Higher dimensional class field theory
8pp.
(Geometric Langlands Seminar, U. of Chicago, 5/00)
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Towards a higher dimensional Langlands program
8pp.
(Geometric Langlands Seminar, U. of Chicago, 5/00)
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Hecke algebras and harmonic analysis over two-dimensional local fields
11pp.
(Geometric Langlands Seminar, U. of Chicago, 3/01)
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Higher dimensional geometric Langlands
11pp.
(DARPA Higher dimensional Langlands meeting, U. of Chicago, 10/04)
- Anton Kapustin :
Topological field theory and Geometric Langlands
(Vienna Geometric Langlands and Physics workshop, 1/07)
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Loop operators
(Vienna Geometric Langlands and Physics workshop, 1/07)
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Holomorphic-topological twist of N=2 gauge theories
(Gauge Theory and Representation
Theory, IAS, 11/07)
- David Kazhdan
Stability of invariant distributions over local fields 2pp.
(AMS meeting, Northwestern U., 10/04)
- Gerard Laumon:
Homologie des Fibres de Springer
(Luminy Langlands Program meeting, 6/06. )
- Kyu-Hwan Lee:
Spherical Hecke algebras of reductive groups over 2-dimensional local fields.
6pp.
(U. of Chicago, DARPA Langlands Seminar 10/04)
- Sergei Loktev :
Current algebras and representations
5pp.
(U. of Chicago, DARPA Langlands Seminar 10/04)
- Andrei Losev:
Quantum field theory for mathematicians I
(Vienna Geometric Langlands and Physics workshop, 1/07)
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QFT for mathematicans II
(Vienna Geometric Langlands and Physics workshop, 1/07)
- Ivan Mirkovic:
Perverse sheaves on a loop Grassmannian
(MSRI Geometric Langlands conference, 3/02. )
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Lie algebras in positive characteristic: geometry and Langlands duality
6pp. (Seattle Algebraic Geometry Summer Institute, 8/05)
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Geometric Langlands in positive characteristic
(Vienna Geometric Langlands and Physics workshop, 1/07)
- Takuro Mochizuki:
Twistor structures and harmonic bundles.
(Vienna Geometric Langlands and Physics workshop, 1/07)
- David Nadler
Real groups and geometric Langlands 3pp.
(AMS meeting, Northwestern U., 10/04)
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Constructible Sheaves and the Fukaya Category
(Vienna Geometric Langlands and Physics workshop, 1/07)
- Bao Chau Ngo:
Fibration de Hitchin et Endoscopie
(Luminy Langlands Program meeting, 6/06. )
- Yan Soibelman:
Lectures on Quantum Groups
(Harvard graduate course, Fall '97. )
- Yakov Varshavsky:
Towards a global Langlands correspondence
(IAS Spring Term 2008)
- Edward Witten:
Gauge Theory and the Geometric Langlands Program I-VII 32pp. (Part II by
Anton Kapustin.
Luminy Langlands Program meeting, 6/06.)
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Gauge Theory and Wild Ramification
(Gauge Theory and Representation
Theory, IAS, 11/07)
- Yongchang Zhu:
p-adic Conformal Field Theory
5pp.
(U. of Chicago, DARPA Langlands Seminar 10/04)