Graduate Seminar. Geometric Representation theory. Fall 2009--Spring 2010

Announcements & Schedule

Links to published books have been de-activated for copyright reasons. Please contact me if you have any questions.

The seminar was devoted to studying the unfinished book by Beilinson and Drinfeld "Quantization of Hitchin's integrable system and Hecke Eigensheaves".

Seminar Notes

The link to the text of the Beilinson-Drinfeld book

Notes from the Spring Semester 2010

If you have any comments on these notes (mathematical, pedagogical or typos), please let me know!

Notes from the Fall Semester 2009

Other notes

Suggested Background Reading

If you are aware of additional/better references on the subjects listed below (especially, number theory), or can provide URL's or .pdf files, please let me know!

Homological algebra

Introduction to derived categories
DG categories


General theory
Nearby and Vanishing cycles
Twisted differential operators (TDO) and D-modules in the equivariant setting

Constructible and perverse sheaves

Constructible sheaves on complex algebraic varieties

See also:
Etale cohomology
Constructible sheaves in the l-adic setting
Perverse sheaves

Algebraic stacks

Descent theory
See also the original article by Grothendieck:
Why do certain moduli problems admit solutions? Quot schemes, Hilbert schemes, Picard schemes, etc.
See also the original (wonderful) articles by Grothendieck:
Definition of stacks
The stack of G-bundles
A good intro to the kind of things we'll be doing is:

Category O

The original papers by Bernstein-Gelfand-Gelfand in Functional Analysis and Applications: See also:

Number theory

Some familiarity with local and global fields, adeles, adele groups and basics of the theory of automorphic functions and representation would be useful.
Local and global fields, adeles
Automorphic functions
Class Field theory
There are numerous expositions. Below is the link to informal lectures by A. Beilinson at U of C: