I will discuss a question raised independently by Greenberg
and Shalom: can a discrete subgroup of a simple Lie group have
dense commensurator and not be a lattice? Both Greenberg and Shalom
seem to believe the answer is yes, so we call this the Greenberg-Shalom
hypothesis. The hypothesis turns out to imply answers to many long
questions in group theory, geometry and topology. I'll start off with a
simple question about pairs of 2 by 2 matrices first raised in the 50's and
60's by Sanov and Lyndon-Ullman and use that to motivate the idea of
commensuration and the Greenberg-Shalom hypothesis.
The talk should be
broadly accessible. Parts of the talk represent joint work with
(subsets of) Brody, Mj and van Limbeek.
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Last modified: April 11 2016 - 18:14:43