Spectral theory and self-similar blowup in wave equations

This is an expository article that describes the spectral-theoretic aspects in the study of the stability of self-similar blowup for nonlinear wave equations. The linearization near a self-similar solution leads to a genuinely nonself-adjoint operator which is difficult to analyze. The main goal of this article is to provide an accessible account of the only known method that is capable of providing sufficient spectral information to complete the stability analysis. The exposition is based on a mini course given at the <italic>Summer School on Geometric Dispersive PDEs</italic> in Obergurgl, Austria, in September 2022.