Number Theory Seminar
Counting closed geodesics and elliptic curves
Speaker: Alberto Acosta Reche (University College of London)Date: Thursday, 12 November 2026 - 11:00Place: Aula 520, departamento de matemáticas, UAM
Abstract:
The prime geodesic theorem (PGT) describes the asymptotic distribution of lengths of closed geodesics on a hyperbolic surface. The vertical Sato--Tate law for elliptic curves (VST) describes the distribution of the normalized traces of Frobenius elements of elliptic curves over a finite field as the cardinality of the field grows to infinity. In the first part of the talk, I will explain my work on estimating the error term in the PGT for Fuchsian groups derived from quaternion algebras. In the second part of the talk, I will explain how an analogy between the PGT and the VST can be used to obtain strong estimates for the discrepancy in the VST.
