Speaker
Pierre-Emmanuel Caprace
Description
$SL(2,R)$ is an example of a hyperbolic locally compact group, i.e. a locally compact group that is Gromov hyperbolic with respect to the word metric associated with a compact generating set. This talk, based on joint work with Mehrdad Kalantar and Nicolas Monod, is devoted to the structure of hyperbolic locally compact groups that are of Type I. The Type I property formalizes the condition that their unitary representations are well behaved. I will discuss a general conjecture predicting that every Type I locally compact group shares a key structural feature with $SL(2, R)$, and outline a proof in the case of hyperbolic locally compact groups containing a uniform lattice.
