# Discrete Subgroups of Lie Groups

### Math 545 - Topics in Riemannian Geometry - Fall 2001

This is an introduction to the theory of lattices in semisimple Lie groups.
I plan to cover the following topics:

- Overview of Riemannian locally symmetric spaces;
- semisimple Lie groups;
- basic properties of lattices;
- arithmetic lattices;
- rigidity and arithmeticity;
- amenability and property (T);
- normal subgroups of higher rank lattices;
- some ergodic theory, as needed.

The main prerequisite is to share a strong liking for groups in general,
and infinite groups in particular. It would help greatly to also have
taken the qual. courses in algebra and geometry-topology.

For most of the course, I plan to use the (unfinished) set of notes
by Dave Witte-Morris:
"Introduction to Arithmetic Groups." It can be downloaded from
here.
(Scroll down to "books in progress.")
I may also take from "Discrete Subgroups of Semisimple Lie Groups," by
G. Margulis.

Classes will be held in a room to be announced, on Mondays, Wednesdays and
Fridays, from 2:00PM till 3:00PM.
If you have questions, please contact
me at
feres@math.wustl.edu or in Cupples I room 17 (phone 5-6752).

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