Dynamics of geodesics, and Maass cusp forms

Abstract

The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide audience of mathematicians---a mathematically rigorous instance of such a relation that emerged in recent years, showing a dynamical interpretation of certain Laplace eigenfunctions of hyperbolic surfaces.

30 pages, 17 figures

References in corpus (3)

• The transfer operator for the Hecke triangle groups
• Eigenfunctions of transfer operators and cohomology
• A realization of the Hecke algebra on the space of period functions for Gamma_0(n)

Cited by in corpus (1)

• Higher rank quantum-classical correspondence