The goal of this talk is to discuss the phenomenon of super-rigidity of representations of lattices in certain Lie groups and how this remarkable phenomenon shows the arithmetic nature of such lattices. We will also discuss the purely group-theoretic notion of commensurability and its relevance to the question of arithmeticity. These wonderful ideas and results are due to Margulis in the late 70s and mid 80s, but for super-rigidity we will follow a more recent approach that we developed with Uri Bader, that is used in the work of Bader-Fisher-Miller-Stover.
Manchester Building (Hall 2), Hebrew University Jerusalem
Alex Fuirman (UIC)