Mathematical Conversations

One of the outstanding insights obtained by physicists working on "Quantum Chaos" is a conjectural description of local statistics of the spectrum of the Laplacian on a Riemannian surface according to crude properties of the dynamics of the geodesic flow, such as hyperbolicity versus integrability. I will describe in general terms what these conjectures say and discuss recent joint work with Valentin Blomer which involves some curious properties of the Fibonacci sequence.