Vorträge in der Woche 04.03.2024 bis 10.03.2024

Dienstag, 05.03.2024: Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic surfaces

Giacomo Gavelli

"This is the first of two talks whose aim is to present a quantum ergodicity theorem for sequences of compact hyperbolic surfaces converging to the hyperbolic plane in the sense of Benjamini-Schramm. The "quantum ergodicity property" is concerned with the distribution of eigenfunctions of the Laplacian on compact Riemannian manifolds. Compact hyperbolic surfaces enjoy the "quantum ergodicity property", and one wants to study the behavior of such a property for sequences of surfaces converging to the hyperbolic plane. The convergence we consider is in the sense of Benjamini-Schramm. In this first talk we introduce the aforementioned notions of quantum ergodicity and Benjamini-Schramm convergence. We then give a broad outline of the proof of the quantum ergodicity theorem, which will be discussed in further details in the second talk."