Seminar: Nondivergence of subgroup action on finite volume homogeneous spaces

Let H be a subgroup of G. Since X is noncompact, one may ask what is the minimal possible H such that every orbit of H intersects a fixed compact subset of X. Together with Han Zhang, we answer this question for H algebraic and connected.

We will review previous work, which deals with special cases, and discuss how one may combine these techniques to give the full proof. We shall also briefly discuss what is known and unknown for other finite volume homogeneous spaces.