Operator and spectral theory of plasmon resonances for structures with corners and edges

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This project aims to investigate the plasmonic eigenvalue problem for objects with corners and edges. Such eigenvalues correspond to surface plasmon resonances, oscillations of electrons, on the interface between different media. The problem will be treated by the use of boundary integral operators.Objectives:(A) To develop the spectral theory for objects with touching corners and edges (for example, bowtie structures).(B) To develop a framework for studying the time-harmonic formulation of the problem for domains with singularities such as corners and edges (as opposed to studying a scale-independent approximation of the problem).