Vorträge in der Woche 11.03.2024 bis 17.03.2024

Dienstag, 12.03.2024: Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic surfaces 2

Giacomo Gavelli

In this talk, the proof of the quantum ergodicity theorem introduced last week is presented. Making use of Selberg's Trace Formula for hyperbolic surfaces, we see that, under Benjamini-Schramm convergence, the number of eigenvalues of the Laplacian in any compact interval grows asymptotically as the volume. Provided this asymptotic estimate, the proof of the quantum ergodicity theorem reduces to an estimate on the Hilbert-Schmidt norm of an averaging operator. This is done by mean of a quantum ergodicity theorem of Nevo.

Donnerstag, 14.03.2024: Eigenvalue estimates on shrinkers

Simon Brendle (Columbia University)

We discuss an eigenvalue estimate which holds for every embedded self-similar shrinker to mean curvature flow. The proof relies on a Reilly-type formula.

Freitag, 15.03.2024: Microscopic derivation of Vlasov equations with singular potentials

Manuela Feistl