Spectral theory of differential operators is a rapidly developing area on the edge between differential equations, mathematical physics, and functional analysis, with applications in many branches of mathematics, mathematical physics and theoretical physics. This workshop focuses on recent developments in the spectral and scattering theory of self-adjoint and non-self-adjoint Schrödinger operators, more general elliptic differential operators, as well as the connections and interplay between spectral theory of differential operators and certain classes of analytic functions, among them the Dirichlet-to-Neumann map and more abstract Titchmarsh--Weyl $m$-functions from modern operator theory. Applications will include resonances in quantum theory, quantum graphs and more general network problems, photonic crystals and quasicrystals.