Math 388-02: Arithmetic Groups
(Feb 11-Mar 18)
Instructor: L. Saper

I am teaching a mini-course on Arithmetic Groups this semester from
February 11 - March 18.  The course will be on Wednesdays and Fridays at
1:15 - 2:30 in Physics 227, beginning next Friday.

If you are interested, please register for the course, Math 388.02, so
that I can gauge interest and background.

The topics to be covered are listed below.  I want to keep prerequisites
to a minimal.  Thus I will cover a number of background topics that
should be of interest to various people in their own right.  Also the
precise topics to be covered in the latter half of the course are not
fixed in stone --- I would like to be guided by people's interests, so
please e-mail me suggestions.

1. Algebraic groups, arithmetic groups (for example, SL_n(Z)
2. Group cohomology
3. Sheaf theory and sheaf cohomology
4. DeRham cohomology with coefficients
5. Lie algebra cohomology
6. Symmetric spaces and locally symmetric spaces
7. Harmonic theory and differential forms on locally symmetric spaces
8. Matsushima-Murakami/Raghunathan vanishing theorem

Subsequent topics may include
- L^2-cohomology
- compactifications of locally symmetric spaces
- intersection (co)homology theory
- reduction theory for arithmetic groups
- survey of the congruence subgroup problem