Mathematical Aspects of Physics with Non-Self-Adjoint Operators: 10 Years After

Significant developments in the spectral analysis of non-self-adjoint operators since the turn of the millennium include the explicit construction of well-localised almost-eigenvectors, the systematisation of the notion of pseudospectra and the rigorous setting of unbounded solvers for evolution problems. At the same time, a deep understanding of complicated physical phenomena such as cloaking in metamaterials, turbulence and explosive behaviour, has been achieved by means of close examination of the underlying non-self-adjoint operators. These developments involve combining techniques from diverse disciplines and in recent years groups who had been working on similar problems from different perspectives, often using different terminology, have been unaware of each other.