# Jerusalem Mathematics Colloquium

Thursday, 13 May 1999, 4:00 pm

Mathematics Bldg., lecture hall 2

##

Dr. Yehuda Shalom

(Princeton University)

"Arithmetic groups"

** Abstract: **

A simple example of an arithmetic group, but one which will
be sufficiently interesting for the purposes of the talk, is the group
SL(n,Z) of determinant one integral matrices. We shall discuss four
properties of arithmetic groups: The congruence subgroup property,
superrigidity, property (T) of Kazhdan, and bounded generation.
Each of these properties involves deep tools from different areas of
mathematics: algebra, geometry, ergodic theory, number theory, group
theory and infinite dimensional representation theory. A phenomenon
which is currently partially explained and partially conjectured, is
that these properties appear together. In the talk we shall carefully
explain all these properties, the connections and conjectures
involved, and some of the recent developments. A background of
undergraduate studies will be more than enough.

Coffee, Cookies, Company at the faculty lounge at 3:30.

List of talks, 1998-99

List of talks, 1997-98