Aleksey Kostenko
University of Ljubljana, Slovenia & University of Vienna, Austria

Generalized indefinite stings, the object introduced by J. Eckhardt and the speaker almost 10 years ago, serve as yet another canonical model of a self-adjoint operator with simple spectrum. One of our main goals in this talk is to overview developments in spectral theory of strings. In particular, we plan to present a characterization of spectral measures/Weyl-Titchmarsh functions of (relative) Hilbert-Schmidt perturbations of some model strings. Our second goal is to demonstrate the application of this result to the Camassa-Holm equation, a remarkable nonlinear wave equation, for which generalized indefinite strings serve as Lax (isospectral) operators. Based on joint work with J. Eckhardt (Loughborough).