Jouni Parkkonen: Counting common perpendiculars in negative curvature

Let M be a complete connected Riemannian manifold with dimension at least 2 and pinched sectional curvature at most -1. I will discuss the asymptotic behaviour of the number of locally geodesic common perpendicular arcs of length at most t between two properly immersed closed convex subsets of M, as t goes to infinity.This is joint work with F. Paulin.