Counting pairs of saddle connections

A translation surface is a collection of polygons in the plane with parallel sides identified by translation to form a Riemann surface with a singular Euclidean structure. A saddle connection is a special type of closed geodesic. I will discuss recent work showing that for almost every translation surface the number of pairs of saddle connections with bounded virtual area has quadratic asymptotic growth. No previous knowledge of translation surfaces or counting problems will be assumed. This is joint work with Jayadev Athreya and Howard Masur.