Livio Flaminio: Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite mixing asymptotics for horocycle flows

We establish an asymptotic expansion of the correlations for the horocycle flow on Abelian covers of compact hyperbolic surfaces. We also prove that the spectra around $0$ of the Casimir operators on any increasing sequence of finite Abelian covers become equidistributed with respect to an absolutely continuous measure. Joint work with D. Ravotti (Wien).