Abstract: In this talk, I will quantitatively relate the resonance sets of certain hyperbolic surfaces to the resonance sets of certain metric graphs via the spine graph construction. Resonance sets of metric graphs are known to contain structures known as ‘resonance chains’, and so as a corollary I will show the existence of approximate resonance chains in resonance sets of these surfaces as specific geometric parameters become large. In the language of zeta functions, these results can be restated in terms of the Selberg zeta functions of these surfaces degenerating to polynomials under an asymptotic limit.
My primary tools will be dynamical zeta functions and a careful analysis of transfer operators arising from holomorphic iterated function schemes. The talk will feature a mix of symbolic dynamics and concrete hyperbolic geometry.
If you are interested in participating online please contact Tobias Weich in order to receive the login details.