Geometric Langlands Seminar
Normally the seminar meets on Mondays and/or Thursdays in
room E206, 4:30
pm--??, where "??" denotes the time when we get tired (e.g., 7:30 pm).
Here are the email
announcements for the current academic year and
information for visitors.
Some texts related to the
talks at the seminar
and Footboards. You might have heard these words mentioned on
the seminar. If you ever wondered what they meant, here's an
- Illusie on Grothendieck's Seminar at IHES (notes in PDF).
Introduction to categorical Kac-Moody actions
- Ivan Losev's notes for his talks on categorical Kac-Moody actions
(April 2013) in PDF
- Automorphic Forms, Representaions, and
of a conference in Corvallis), A.Borel and W.Casselman (editors), AMS,
useful for those intereseted in the Langlands program. PDF
from the AMS site: Volume
- Algebraic Groups and Discontinuous Subgroups,
A.Borel and G.Mostow
(editors), AMS, 1966. PDF available from the
Fundamental Lemma and Endoscopy (new version!)
- Le Lemme Fondamental pour les
Algebres de Lie, Bao Chau Ngo, e-print available here
- Drinfeld's notes on the local Tate-Nakayama duality and its
interpretation due to Kottwitz: PDF
- The article by Kottwitz mentioned in these notes: PDF
- Drinfeld's notes on Kostant's theorem: PDF
- The e-print by Beilinson and Drinfeld mentioned in these notes is
- Drinfeld's notes on centralizers of semisimple elements of
semisimple groups: PDF
- Drinfeld's notes in which he reformulates (a part of) the
Fundamental Lemma for SL(n) in very concrete and "classical" terms: PDF
- An example of an endoscopy group that is not a subgroup of the
ambient group: PDF
- Drinfeld's notes for his lecture on regular centralizers: PDF
- Drinfeld's notes for his lecture on the Hitchin fibration: PDF
Some useful books available online
(but the quality is not very good).
- Current Trends in Arithmetical Algebraic
Geometry, K. Ribet (editor),
AMS, 1987. PDF available from the
- Invitation to higher local fields,
I.Fesenko and M.Kurihara (editors).
Available as PS or PDF from the
Derived category of quasicoherent sheaves
- Synopsis of Bezrukavnikov's talks on the Thomason-Trobaugh
Theorem (DVI, PostScript).
- Notes on Quillen's constructions of K-groups (DVI, PostScript).
- Beilinson's comments on Bloch's lecture of 11.3.03 (DVI, PostScript).
- J.Morava's notes on cobordism theory. (DVI, PostScript).
Updated on 08/02.
- V.Voevodsky, Lectures in Motivic Cohomology.
C.Mazza and C.Weibel, available on Weibel's
- M.Kontsevich's course at ENS, 1998 (French).
Course notes in PostScript.
A related letter from M.Kontsevich to A.Beilinson. Text.
- R.Nest and B.Tsygan, Cyclic Homology.
- V.Drinfeld, DG quotients of DG categories. E-preprint.
- B.Keller, Introduction to A-infinity algebras
and modules. E-preprint.
- K.Lefevre-Hasegawa, Sur les A-infini categories.
- M.Kontsevich's course on deformation theory. Course notes in PostScript.
- V.Ginzburg, Lectures on noncommutative geometry. E-preprint.
- A.Bondal, M.Van den Bergh, Generators and
representability of functors
in commutative and noncommutative geometry. E-preprint.
- The derived category of finite-dimensional representations
of a quiver
is an important and somewhat unusual example of a smooth proper DG
home page , the Miyachi-Yekutieli e-print math.RA/9904006 ,
the Appendix of Yekutieli's e-print math.RA/9810134,
and pages 13, 16-18, 21, 23, 24 of Kontsevich's
- Notes of Arinkin's talk on deformation qunatization and
the Fourier-Mukai transform
(04/06/06). (DVI, PostScript).
Some lecture notes and articles by Joseph
- Course on D-modules (PostScript, DVI).
- Course on representations of p-adic groups (PostScript, DVI).
- Second adjointness for representations of reductive p-adic
- Meromorphic continuation of Eisenstein series: Lecture I
The determinant of cohomology and
microlocalization (after A. Beilinson)
- A. Beilinson, Topological $\epsilon$-factors. E-preprint.
- `Appendix: The case of a surface' by A. Beilinson (PDF).
Epsilon-factors for the period
determinants on curves
This section contains some notes
related to Alexander Beilinson's lectures in the seminar in the spring
quarter of 2008.
- PDF scans of Laumon's notes of Deligne's talks on the period
determinants (Spring 1984):
Some texts by Beilinson and Drinfeld
Geometric Langlands conjecture and
- V.Drinfeld, Infinite-dimensional vector bundles
in algebraic geometry, notes of the talk at the `Unity of
version: (PostScript, PDF).
- Pavel Etingof's notes for his lecture "Solvable fusion categories
and a categorical Burnside's theorem" (PDF)
Some very basic lectures on
spectra and K-theory
- K-theory of a Waldhausen
category as a symmetric spectrum (PDF)
- Introduction to symmetric spectra I (PDF)
to symmetric spectra II (PDF)
- Picard groupoids and spectra (PDF)
These are notes for lectures given in
the seminar by M. Boyarchenko in the spring of 2006. The notes contain
no original results, and probably do contain lots of mistakes.
Use at your own risk. All comments are welcome.
- M. Boyarchenko: notes for the series of lectures
"Introduction to modular categories" (Lecture
1, Lecture 2, Lecture 3).
- D. Nikshych: Morita duality for fusion categories and the
geometry of modular categories (Lecture
1, Lecture 2).
- M. Boyarchenko: notes for the lecture "Modular categories and
modular functors" (PDF).
This page is maintained by Mitya Boyarchenko.
Last updated on 10/02/2007.