Spectral stability and instability of finite Riemannian coverings

The pull-back of an eigenfunction from the base $M$ of a Riemannian covering to the covering manifold $M'$ is an eigenfunction on $M'$. In the talk, I will discuss the existence of new eigenfunctions on $M'$. This is joint work with Sugata Mondal and Panagiotis Polymerakis.