The complex modular curve is a non-compact hyperbolic surface that plays a fundamental role in number theory and homogeneous dynamics. The periodic geodesics on the modular curve carry important information about real quadratic fields and their class groups. I will introduce these objects and will discuss two perspectives on the equidistribution of packets of closed geodesics: a dynamical approach going back to Linnik in the 50's and a harmonic analytic approach which culminates in Duke's theorem from the 80's. Speaker(s): Ilya Khayutin (Northwestern)