Mathematical Sciences: Spectral and Variational Problems of Mathematical Physics

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This mathematical research project will undertake spectral and variational analysis of several topics originating in theoretical physics. It is both pure and applied mathematics: applied in the sense that one of the goals is the derivation of formulae that a physicist can actually use, and pure in that it consists of proving rigorous theorems. Quantities of physical importance are frequently minimizers of certain functionals or eigenvalues and eigenvectors of linear operators. In this research most of them originate in quantum physics, such as Schroedinger operators for individual particles or bulk matter, or the Skyrme model for baryons. The principal investigators will continue their work on these and other subjects by combining abstract techniques, primarily from functional analysis, with more particular tools, e.g. from the theory of differential equations or perturbation techniques. Intuition from physics and from numerical calculations is also expected to help.