Logic Seminar

Given a countable group Gamma, there is a compact space of subgroups Sub(Gamma), which is equipped with the Gamma-action via conjugation. We study the notion of weak containment on this space, namely when one subgroup is contained in the orbit closure of another, which is related to weak containment of quasi-regular unitary representations of Gamma. In particular, we will consider necessary and sufficient conditions for the existence of dense orbits.