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have other comments, thanks!
See also the containing a large and growing collection of lecture
notes, with a strong emphasis on geometric Langlands topics. In particular
this collection includes (close
to) complete notes from Geometric Langlands conferences in
Vienna (2007), Luminy (2006), and Berkeley (2003).
My Selected Lectures:
Lecture notes and videos from the
2007 London Math Society Invited Lecture Series are
Topological Field Theory and Geometric Langlands: notes
and audio and video
from a lecture series at the
KITP Santa Barbara workshop on Geometric Langlands and Gauge Theory, July 2009.
Introduction to Geometric Langlands, notes from lecture
at the Vienna workshop on Geometric Langlands and Physics, January 2007.
Lectures from the Gottingen Winterschule on Geometric Langlands:
Geometric function theory,
Geometric Langlands and Topological Field Theory
Geometric Langlands and Real Groups.
A three-part introduction to the
geometric Langlands program I gave in 2002 is available on streaming video
courtesy of MSRI:
Class Field Theory, Quantization
of Hitchin's Hamiltonians, and Factorization.
The February 2005
Talbot workshop (for
which I was the plenary speaker) provided an intense "Geometric
Langlands retreat" for graduate students.
There are notes available as one
huge file or as individual
pages courtesy of Megumi Harada.
the deal with Geometric Langlands?: lecture notes taken by Parker
Lowrey for a talk I gave at the Algebraic Geometry Boot
Camp, a warmup workshop for graduate students attending the 2005
AMS Summer Institute in Algebraic Geometry, Seattle.
Langlands Program, audio for a lecture I gave at the
Workshop on Forms of Homotopy Theory: Elliptic Cohomology
and Loop Spaces at the
Fields Institute in Toronto, 2004.
Other Geometric Langlands Resources:
Chicago Geometric Langlands Page contain many useful links and references.
Here are links to the ICM addresses of
related to geometric Langlands.
Gerard Laumon's Bourbaki talk
Travaux de Frenkel, Gaitsgory et Vilonen sur la correspondance de Drinfeld-Langlands
surveys the proof of the geometric Langlands conjecture for GL_n.
( arxiv search)
several excellent survey articles on aspects of the geometric
Here are other (also related) surveys by Frenkel:
Lectures on the Langlands Program and Conformal
Field Theory. hep-th/0512172
Recent Advances in the Langlands Program. Bull Amer. Math. Soc.
41 (2004) 151-184. Journal
Affine Algebras, Langlands Duality and Bethe Ansatz. XIth
International Congress of Mathematical Physics (Paris 1994)
606--642. International Press, Cambridge MA 1995. math.QA/9506003.
Here are files of two works by A. Beilinson and
V. Drinfeld (posted with the authors' permission).
(Most of these are g-zipped postscript -
to read these, apply "gunzip (filename)" to obtain a postscript file.)
Algebras (version: 9/00 --- far from the published final version), and
Quantization of Hitchin's Integrable System and Hecke Eigensheaves (uncompressed pdf version),
Quantization of Hitchin's Integrable System and Hecke Eigensheaves (gzipped ps version)
(version: 2/00) These files are quite large - to get 100 pages at a
time, download the following: Hitchin
Pages 1-100, Hitchin
Pages 101-200, Hitchin
Pages 201-300, and Hitchin
Pages 1-100, Chiral
Pages 101-200, and Chiral
Geometric Langlands on TV: In Episode 11 of Season 4 of Fox's
"24", we find Drinfeld modules, the central construction in the
solution of the Langlands program over function fields (by Drinfeld
for GL 2 and Lafforgue for GL n), in use by the
Counter Terrorist Unit, spearheaded by Kiefer Sutherland's character
Jack Bauer. One of the terrorists explains to his boss about CTU
foiling their efforts: "Using a Drinfeld module they've already shut
down over 90 reactors" (see a blog review).
Interestingly, an online transcript of the show
differs from the script and subtitles, and mentions instead a
"dreen-filled mode tool" (see an
unofficial transcript). Disclaimer: To the extent of my knowledge,
the relevance of Drinfeld modules to national security is an original
contribution of "24".
David Goss kindly provided
the backstory for this mysterious appearance of Drinfeld modules:
"I grew up in the Detroit area with a number of great people who have
gone on to great things; some of them in showbiz. My dear friend Michael
Loceff is one such. He and I studied math together at Michigan.
After a few years Michael lost interest in his studies and
went on to other things. He teaches computer science over the web at
college using software he wrote. Michael's cousin is Joel Surnow and
Michael started to write with Joel on "La femme Nikita" and now
Michael is an executive producer and write for 24. So you can imagine
where the mention of Drinfeld modules arose! ... Finally,
Michael likes to use names of people he grew up with
in the show. In one episode at the beginning of season 2 or 3 (I never saw
it) there is a dead drug dealer named "David Goss" and Jack Bauer goes
around asking people if they knew this drug dealer.... One has to have a
sense of humor."
Assorted introductions and surveys on related topics:
(Please send suggestions to add!)
Dennis Gaitsgory's suggested background readings.
Notes on Grothendieck topologies, fibered categories and descent
-Herb Clemens, Aaron Bertram et al.
Park City Math Institute Notes on Stacks
-Tomas Gomez: Algebraic stacks
-Barabara Fantechi: Stacks for Everybody (Park City 2001 proceedings)
-Bertrand Toen: Course on
-William Fulton: Introduction to Stacks
(from a long-term book project)
-Claudia Centazzo and Enrico Vitale:
Theory (from a topos theoretic point of view).
-Joseph Bernstein: Course on D-modules. (The classic reference.)
-Dragan Milicic: Lectures on Algebraic Theory of D-Modules
-Philippe Maisonobe and Claude Sabbah:
Aspects of the theory of D-modules
An introduction to D-modules
Geometric Representation Theory:
Course on Beilinson-Bernstein theory
-Dragan Milicic: Algebraic D-modules and representation theory of semisimple
Lie groups. (Overview article)
-Dragan Milicic: Localization
and represention theory of reductive Lie groups. (Book.)
Gradings on Representation Categories (ICM address)
Methods in Representation Theory (Park City lectures). See also
his ICM address Topological Methods in Representation
-Matvei Libine and Wilfried Schmid,
Geometric Methods in Representation Theory.
-Vernon Bolton and Wilfried Schmid,
-Hiraku Nakajima: Geometric
construction of representations of affine algebas (ICM address).
An introduction to perverse sheaves.
-David Massey: Notes on perverse sheaves and vanishing cycles.
-David Massey: Stratified Morse theory: past and present .
Derived Categories, Model Categories etc:
Graded Categories (ICM address).
-Alexei Bondal and Dimitry Orlov: Derived
categories of coherent sheaves (ICM address).
Derived categories of sheaves: a skimming.
Derived Categories for the Working Mathematician
-Paul Goerss and Kristen Schemmerhorn:
Model Categories and Simplicial Methods
resolutions and Brown representability (see also the
Spectra for commutative algebraists
Notes on Derived Categories and Derived Functors
History of homological algebra
course on homological algebra (see also his course on algebraic
-Pierre Schapira: Courses on
categories and homological algebra,
sheaf theory, and algebraic
Moduli of Bundles:
-Christoph Sorger: ICTP
Lectures on moduli of principal G-bundles over
-Gerd Faltings: Vector Bundles on Curves (course notes).
-Ron Donagi and Eyal
Markman: Spectral curves, algebraically completely integrable Hamiltonian systems, and moduli of bundles.
Hecke Algebras: -Tom Haines, Robert Kottwitz and Amritanshu
-Victor Ginzburg: Geometric
methods in representation theory of Hecke algebras and quantum groups
-Alexandre Stefanov maintains an excellent collection of links to
textbooks in math.
-Igor Dolgachev's lecture notes page has excellent courses on physics
and string theory, invariant theory, and algebraic geometry.
-Franz Lemmermeyer's lecture
notes page and course notes
page host a large collection of links to courses and notes, mainly
related to algebraic geometry and number theory.
Number of visitors to my page:
Department of Mathematics
University of Texas, Austin
University of Texas, Austin Mathematics Department
Created: March 9 2005 ---
Last modified: May 28 2006