Effective density of unipotent orbits in homogeneous spaces

Let X be a homogeneous space of finite volume, i.e. the quotient of a Lie group G by a lattice in G.
In this talk we will present a work in progress with Lindenstrauss, Margulis and Shah,
which provides an estimate on how large a piece of a unipotent orbit is needed
so that it comes within epsilon distance of any point in a given compact subset of X.
This estimate depends on a certain diophantine property of the base point and the acting unipotent group.

This talk is supported by the Mrs. Hepsa Ely Silliman Memorial Fund