Resonances of Schottky surfaces
Mathematical Physics Seminar
5th March 2021, 2:00 pm – 3:00 pm
Online seminar, Zoom
Resonances of the Laplacian of Riemannian manifolds are of great importance in many areas of mathematics and physics. Even though many fascinating results about these spectral entities have already been found, an enormous amount of their properties, also some very elementary ones, is still undiscovered. A few years ago, by means of numerical experiments, Borthwick noticed for some classes of Schottky surfaces (certain hyperbolic surfaces of infinite area) that their sets of resonances exhibit unexcepted and nice patterns, which are not yet fully understood.
After a brief survey of some parts of this field, we will discuss an alternative numerical method, also motivated by physics, combining tools from dynamics, zeta functions, transfer operators and thermodynamic formalism, functional analysis and approximation theory. The emphasis of the presentation will be on motivation, heuristics and pictures. In particular, no prior knowledge on Schottky surfaces or other Riemannian manifolds, their spectral theory, resonances, etc is assumed. This is joint work with Oscar Bandtlow, Torben Schick and Alex Weisse.