Shrinking target problems for homogenous flows

In this talk I will describe joint work with Shucheng Yu, on shrinking targets problems for discrete time flows on a homogenous space $\Gamma \bk G$ with $G$ semisimple group and $\Gamma$ an irreducible lattice. Our results apply to both diagonalizable and unipotent flows, and apply to very general families of shrinking targets. As a special case, we establish logarithm laws for cusp excursions of unipotent flows answering a question of Athreya and Margulis.