Lecture Notes on Representation theory and Geometric Langlands

Lecture Notes from the Special Year on New Connections of Representation Theory to Algebraic Geometry and Physics. Institute for Advanced Study, 2007-8.

Notes from Vienna workshop on Geometric Langlands and Physics, January 2007

Notes from Gottingen Winterschule on Geometric Langlands, January 2007

• Alexander Beilinson: Quantization of Hitchin Hamiltonians and Hecke Eigensheaves (MIT, Kac Seminar, 10/95)
• Chiral Algebras and Hecke Eigensheaves (Brandeis, Colloquium, 4/96)
• Chiral Hecke Algebras (IAS, Langlands birthday conference, 10/96)
• Hecke Eigensheaf Property 11pp. (IAS, Langlands seminar, 4/97 - sequel to Drinfeld lectures on Quantization)
• Introduction to Geometric Langlands 21pp. (U. of Chicago Geometric Langlands seminar, 10/99)
• Nearby Hecke Functors and Kac-Moody Modules 4pp. (U. of Chicago Geometric Langlands seminar, 6/00)
• Triangulated categories 16pp. (U. of Chicago Geometric Langlands seminar, 11/01)
• Differential operators on ind-schemes 12pp. (U. of Chicago Geometric Langlands seminar, 11/03)
• On the Langlands Correspondence in the de Rham Setting, I and II (MSRI Geometric Langlands conference, 3/02)
• Topological Epsilon Factors (Luminy Langlands Program meeting, 6/06)
• Connections on the punctured disc (Evanston Noncommutative Geometry Conference, 5/07)
• 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)
• Geometric Langlands and Positive Characteristic (Luminy Langlands Program meeting, 6/06)
• Local Geometric Langlands Correspondence (Vienna Geometric Langlands and Physics meeting, 1/07)
• Stability Conditions (IAS Spring Term 2008)
• Stability Conditions II (IAS Spring Term 2008)
• 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. )
• 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)
• 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)
• Quantization of Hitchin's Hamiltonians and Opers, Parts I-IV 17pp. (IAS, Langlands seminar, 3/97)
• Lectures on DG Categories 23pp. (U. of Chicago Geometric Langlands seminar, 10/02)
• 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)
• 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)
• Geometric Langlands and Affine Kac-Moody Algebras I-II 7pp. (Northwestern University, 4/02)
• Critical Level Representations and Local Langlands I-II 13pp. (U. of Chicago, DARPA Langlands meetings, 11/03. With comments by Drinfeld and Bezrukavnikov.)
• 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)
• 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)
• Local Geometric Langlands 7pp. (U. of Chicago, DARPA Langlands Seminar 11/03)
• Two-dimensional Geometric Langlands? 3pp. (U. of Chicago, DARPA Langlands Seminar 10/04)
• de Jong's Conjecture 4pp. (AMS meeting, Northwestern U., 10/04)
• Lecture Series on Beilinson-Bernstein Localization for Loop Groups 39pp. (U. of Chicago Geometric Langlands Seminar 10/04)
• 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)
• Symplectic Reflection Algebras I-IV 21pp. (Geometric Langlands Seminar, U. of Chicago, 11/00)
• Vanishing Cycles for D-Modules 13pp. (Lectures from a graduate course, U. of Chicago, Spring 2001)
• 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)
• Tamely ramified Langlands II (Vienna Geometric Langlands and Physics workshop, 1/07)
• Tamely ramified Langlands III (Vienna Geometric Langlands and Physics workshop, 1/07)
• 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)
• Towards a higher dimensional Langlands program 8pp. (Geometric Langlands Seminar, U. of Chicago, 5/00)
• Hecke algebras and harmonic analysis over two-dimensional local fields 11pp. (Geometric Langlands Seminar, U. of Chicago, 3/01)
• 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)
• Loop operators (Vienna Geometric Langlands and Physics workshop, 1/07)
• 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)
• 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. )
• Lie algebras in positive characteristic: geometry and Langlands duality 6pp. (Seattle Algebraic Geometry Summer Institute, 8/05)
• 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)
• 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.)
• 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)