In this talk we study the extreme value law for cusp excursions of certain unipotent actions on the space of lattices. We analyze this problem in terms of the hitting time and impact statistics for the unipotent action with respect to a shrinking surface of section, following the strategy of Pollicott and Marklof. 

We will also discuss the asymptotics of the corresponding limiting distribution, which in a special case agrees with the directional statistics of Euclidean lattices. 

This is joint work with Jens Marklof and Andreas Strömbergsson.