The conference is intended as a follow-up of a highly successful series of meetings organised in various places in Europe and North America during the last dozen years, including two CIRM conferences in 2017 and 2021. The goal is to facilitate interdisciplinary collaborations across the mathematical analysis and mathematical physics communities, with a central role being played by the theory of non-self adjoint operators. From the point of view of applications, modern physical subjects, such as advanced structures in condensed matter physics and optics, unconventional representations of observables in quantum mechanics, and non-linear phenomena in hydrodynamics are covered. High impact mid-term aspirations include the development of rigorous tools allowing understanding of complicated physical phenomena including cloaking, turbulence and explosive behaviour. On the mathematical side, invited participants are experts in mathematical physics, microlocal, semiclassical, functional and harmonic analysis, as well as dynamical systems and partial differential equations.