Non-vanishing of geodesic periods of automorphic forms

The study of the distribution of Heegner points and closed geodesics is an important and rich subject, at the confluence of arithmetic, geometry and dynamics. In this work, we use techniques from all these areas to study the distribution of automorphic periods associated to closed geodesics on the modular surface. In particular, we show that 100% of such periods are non-vanishing when ordered by length. We also obtain applications towards non-vanishing of central values of Rankin-Selberg L-functions. Joint work with Asbjørn Nordentoft.