Large covers and resonances of hyperbolic surfaces

In this talk, after a brief refresher on the spectral theory ofinfinite area surfaces, we will investigate the behaviour ofresonances for families of Galois covers of a given surface when thedegree goes to infinity. In particular we will prove a “Weyl Law”for large covers, and an existence result of non-trivial sharpresonances in the case of congruence subgroups.