Spectral approximation on metric graphs, on manifolds, and for systems of differential equations
This project is advertised as part of the EPSRC Doctoral Training Partnership. It is currently not available to self-funded applicants.
The student will acquire a good working knowledge of the mathematical analysis behind some of the fundamental differential equations of mathematical physics, eg Schroedinger, Maxwell and Dirac systems, including some of the most up-to-date ideas from soft analysis such as the very new concept of essential numerical range for unbounded operators and its use in the analysis of numerical approaches to approximation and calculation of spectra.
The student will have the opportunity to learn about finite difference and finite element methods and to acquire programming skills which would transfer to engineering applications. A good calibre student will be encouraged in the last year to apply for an LMS postdoctoral mobility grant and an EPSRC postdoctoral fellowship.