Equidistribution: number theory and dynamics (by Valentin Blomer, universität Bonn)

The modular curve X, i.e. the upper half plane modulo the action of the group of the SL(2, Z), is a Riemannian manifold with rich arithmetic structure. Classical results state that low-lying horocycles and closed geodesics of growing length become equidistributed. In this talk, I will focus on mixing properties of such equidistribution results. A protoype are two horocycles of different speeds.