The interplay of the geometric and the spectral properties of Riemannian manifolds are highly influential in essentially all areas of mathematics, but are far from being fully understood. Some of the recent advancements in understanding this relation could be achieved by means of transfer operators. I shall overview some recent developments in this area with a focus on hyperbolic surfaces, automorphic functions, resonances and the dynamics of the geodesic flow and with an emphasis on insights and heuristics. In particular, I will, at the example of Hecke triangle groups, discuss how an outer symmetry in the dynamics translates into a parity for automorphic functions.

Location: https://meet.google.com/you-qymk-ybu