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".
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
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!
Introduction to derived categories
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
- "Sheaves on Manifolds" by M. Kashiwara and P. Shapira
- "Sheaves in Topology" by A. Dimca (.pdf is available)
- Notes by L. Nicolaescu
Constructible sheaves in the l-adic setting
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:
The original papers by Bernstein-Gelfand-Gelfand in Functional Analysis and Applications:
- "Structure of representations that are generated by vectors of higher weight"
- "A certain category of g-modules"
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
- Volume 6 of "Generalized functions" by Gelfand, Graev and Piatetskii-Shapiro.
Class Field theory
There are numerous expositions. Below is the link to informal lectures by A. Beilinson at U of C: