Abstract: In this talk we discuss a recent result on the representation of
the scattering matrix in terms of an abstract Weyl function. The general result
can be applied to scattering problems for Schrödinger operators with $\delta$-type
interactions on hypersurfaces, and scattering problems involving Neumann and
Robin realizations of Schrödinger operators on unbounded domains. In both
applications we obtain formulas for the corresponding scattering matrices in
terms of Dirichlet-to-Neumann maps. This talk is based on joint work with
Mark Malamud and Hagen Neidhardt.