Notes from Graduate Courses:

• Alexander Beilinson: Course on Chiral Algebras, Part 1 35pp. and Part 2 21pp. (MIT, Fall 1995)
• Tony Pantev: Course on Hodge Theory etc, Part 1 36pp., Part 2 42pp. (MIT, Spring 1996)
• Sasha Polishchuk: Course on Perverse Sheaves, Part 1 35pp., Part 2 47pp., Part 3 31pp. (Harvard, Fall 1996)
• Robert Kottwitz: Course on Deligne-Lusztig Theory and Character Sheaves, Part 1 31pp., Part 2 26pp. (U. of Chicago, Spring 2001)

My Selected Lecture Notes:

Lectures on Representation theory and Geometric Langlands

Lectures on Homotopy Theory

Lectures on Physics

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

• Tom Nevins and I organized a Special Session on Algebraic Geometry, Representation Theory and Topological Field Theories at the March 2009 UIUC regional meeting of the AMS. See notes from the workshop.

  Northwestern Conference on Noncommutative Geometry

  Michigan Conference on D-Bundles and Integrable Hierarchies

  Texas Algebraic Geometry Symposium (TAGS 2007)

• Tom Bridgeland: Stability Conditions I-II 15pp. (U. of Chicago Geometric Langlands seminar, 11/02)
• Lecutres on Flops, Fourier Transforms and McKay Correspondence 14pp. (U. of Chicago Geometric Langlands seminar, 11/02)
• Derived Categories in Algebraic Geometry ( UT Austin GRASP lecture, 9/07)
• Joyce's work on counting invariants and wall-crossing. (Texas Algebraic Geometry Symposium, UT Austin 3/07)
• Kevin Costello: TCFTs and Calabi-Yau Ainfty Categories 8pp. (UT Austin Geometry Seminar, 12/05)
• Discussion on Gromov-Witten Theory 4pp. (UT Austin Geometry Seminar, 12/05)
• Renormalization in the BV Formalism (Northwestern University Noncommutative Geometry Conference, 5/07)
• Renormalization in the BV formalism (UT Austin Geometry and Strings Seminar, 9/07)
• Rational Homotopy Theory and Chern-Simons Theory (UT Austin Geometry Seminar, 9/07)
• Topology in two dimensions and Frobenius algebras ( UT Austin GRASP lecture, 9/07)
• Matthew Emerton: p-adic Langlands - Global Motivations 5pp. (Luminy Langlands Program meeting, 6/06)
• Gavril Farkas: M22 is of general type (UT Austin GADGET seminar, 10/06)
• Koszul divisors on moduli spaces (Clay Foundation meeting on Vector Bundles on Curves, 10/06)
• Strange Duality (UT Austin GADGET seminar, 12/06)
• Tom Hales: Motivic integration and applications 6pp. (AMS meeting, Northwestern U., 10/04)
• Michael Harris: Automorphic Galois Representations and the Sato-Tate Conjecture 7pp. (Luminy Langlands Program meeting, 6/06)
• Magnetic Wilson loops and Montonen-Olive Duality 7pp. (UT Austin Theory Group Seminar, 9/05)
• Mikhail Khovanov: Link homology theories (UT Austin Geometry Seminar, 10/06)
• Maxim Kontsevich: Categorification, NC Motives, Geometric Langlands and Lattice Models 21pp. (U. of Chicago Geometric Langlands Seminar, 2/06)
• Donaldson-Thomas invariants 1 (Workshop on Homological Mirror Symmetry, U. of Miami, 1/08) Notes by David Nadler.
• Donaldson-Thomas invariants 2 (Workshop on Homological Mirror Symmetry, U. of Miami, 1/08) Notes by David Nadler.
• Donaldson-Thomas invariants 3 (Workshop on Homological Mirror Symmetry, U. of Miami, 1/08) Notes by David Nadler.
• Alina Marian: The Strange Duality Conjecture (Clay Foundation meeting on Vector Bundles on Curves, 10/06)
• Tony Pantev D-Branes and Higgs Bundles I-IV 21pp. (UC Santa Barbara Summer School on Geometry and Physics, 8/03)
• Noncommutative Geometry and Framed Sheaves 24 pp. (U.T. Austin Geometry Seminar, 4/04)
• Mihnea Popa: Fourier-Mukai transforms and generic vanishing (UT Austin Geometry Seminar, 9/06)
• Graeme Segal: Locality in Quantum Field Theory I (UT Austin GADGET Seminar, 11/06)
• Locality in Quantum Field Theory II (UT Austin Geometry and Strings Seminar, 11/06)
• Locality of the space of quantum states (Aspen Center for Physics, 8/04)
• Yan Soibelman: Quantization of Calabi-Yau varieties (Northwestern conference on Noncommutative Geometry, 5/07.)
• Noncommutative Geometry of Collapsing CFT (Northwestern conference on Noncommutative Geometry, 5/07.)
• Donaldson-Thomas Invariants. (UT Austin Geometry Seminar, 11/07)
• Constantin Teleman: Twistings in Gromov-Witten Theory 5pp. (Toronto workshop on Loop Spaces and Homotopy Theory, 10/04)
• The structure of semisimple 2d topological field theories 8pp. (UT Austin Geometry Seminar, 4/05)
• Boris Tsygan: Lecture Series on Cyclic Homology and Noncommutative Geometry 24 pp. (U. of Chicago Geometric Langlands seminar, 1-2/03)

Related Notes by Others:

• Notes by Kevin McGerty for 2005 Tel Aviv meeting on works of Bezrukavnikov, 21pp.