Alex Furamn (UIC)
Hidden symmetries of groups and super-rigidity

Abstract:
In the 1970s G.A.Margulis proved that linear representations of
certain discrete subgroups (lattices) in such Lie groups as
SL(3,R), are essentially determined by representations of the ambient Lie group.
This phenomenon, known as superrigidity, has far reaching applications
and has inspired a large body of research in such areas as geometry,
dynamics, descriptive set theory, operator algebras etc.

We shall try to explain the superrigidity of lattices and related
groups by looking at some hidden symmetries (Weyl group) that they
inherit from the ambient group.

The talk is based on a joint work with Uri Bader.