This workshop was a follow-up to the ESF-funded Exploratory Workshop held in Prague 2010. The main objective was to facilitate interdisciplinary collaborations across the mathematical physics community and the mathematical analysis community. This workshop addressed modern techniques for the mathematically rigourous justifcation of non-self-adjoint phenomena encountered in the newly developing fields of: PT-symmetric quantum mechanics, metamaterials, superconductivity, porous media and hydrodynamics.