Effective counting of simple closed geodesies on hyperbolic surfaces: Alex Eskin and Amir Mohammadi dedicate this paper to the memory of Maryam Mirzakhani.

We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most L on a compact surface equipped with a Riemannian metric of negative curvature. The proof relies on the exponential mixing rate for the Teichmüller geodesic flow. [ABSTRACT FROM AUTHOR]