Description:

Title: Zelditch's trace formula and effective equidistribution of closed geodesics in hyperbolic surfaces

Abstract: In the early 1990s, Zelditch modified the Selberg trace formula to prove an effective version of Bowen's equidistribution theorem for closed geodesics on hyperbolic surfaces. In joint work with Junehyuk Jung and Peter Zenz, we refined Zelditch’s argument to obtain the optimal error bound for the equidistribution of closed geodesics on compact hyperbolic surfaces. In this talk, we will review some fundamentals of trace formulas and discuss the main new contributions of this work—from the perspective of the speaker, whose background knowledge was primarily in dynamical systems and low-dimensional topology and geometry prior to this project