Quantum Ergodicity: from geodesic flow to Weyl's lawMPIM

by Eva-Maria Hekkelman (MPIM)

Tuesday Jul 7, 2026, 4:30 PM → 5:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Reading group on spectral geometry 

On compact Riemannian manifolds, a fascinating connection has been found between geodesic flow and the eigenfunctions of the Laplace operator. If the geodesic flow is ergodic, the eigenfunctions corresponding to large eigenvalues will spread 'evenly' over the manifold. I will explain how to make this precise, and in particular how the latter can be seen as a stronger version of Weyl's law. This result from the '80s by Shnirelman, Zelditch and Colin de Verdière was the start of the field that is now called Quantum Ergodicity, and I will showcase some current conjectures and developments in the area.