Pre-lectura de tesis:  Alba Dolores García Ruiz (ICMAT)

Date: 19/05/2025
Time: 11h

Room: 520, Modulo 17, UAM

Title: High-Energy Eigenfunctions of the Laplacian:   Localization Properties and Relation with Berry’s Random Wave Model

Abstract: Berry's random wave conjecture states that high-energy eigenfunctions of chaotic systems behave like random monochromatic waves at the Planck scale. One notable consequence is that, at an appropriate scale, solutions to the Helmholtz equation can be locally approximated by high-energy eigenfunctions around a large set of points in the manifold. This phenomenon, sometimes referred to as inverse localization, has been investigated in various settings, with both positive and negative results depending on the context. In this thesis, we further explore the inverse localization property, its connection to Berry's random wave conjecture, and its implications for the study of nodal sets of eigenfunctions.