Numerics for resonances of Schottky surfaces
A talk in the Kolloquium Mathematische Physik series by
Anke Pohl from Bremen
| Abstract: | Resonances 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 unexpected and nice patterns, which are not yet
fully understood. After a survey of some parts of this field, we will discuss an alternative numerical method, combining tools from dynamics, zeta functions, transfer operators and thermodynamic formalism, functional analysis and approximation theory. This is joint work with Oscar Bandtlow, Torben Schick and Alexander Weiße. |