Shrinking targets problems for flows on homogeneous spaces

We study shrinking targets problems for discrete time flows on a homogenous space $\mathrm{\Gamma }\mathrm{\backslash }G$ with $G$ a semisimple group and $\mathrm{\Gamma }$ 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.