Effective equidistribution of orbits under semisimple groups on congruence quotients

Abstract

We prove an effective equidistribution result for periodic orbits of semisimple groups on congruence quotients of an ambient semisimple group. This extends previous work of Einsiedler, Margulis and Venkatesh. The main new feature is that we allow for periodic orbits of semisimple groups with nontrivial centralizer in the ambient group. Our proof uses crucially an effective closing lemma from work with Lindenstrauss, Margulis, Mohammadi, and Shah.