Zelditch’s Trace Formula and Effective Equidistribution of Closed Geodesics on Hyperbolic Surfaces
ABSTRACT
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In the early 1990s, Zelditch modified the Selberg trace formula to establish an effective version of Bowen’s equidistribution result for closed geodesics on hyperbolic surfaces. Expanding on his framework, and in joint work with Junehyuk Jung and Peter Zenz, we have refined this method to obtain the optimal error bound in the equidistribution of closed geodesics on compact hyperbolic surfaces. This talk will begin with an introduction to the fundamentals of trace formulas and then highlight new advancements. No prior background knowledge of trace formulas is assumed.