Spectral geometry

Supervisor(s)

Contact Dr Gerasim Kokarev to discuss this project further informally.

Project description

Spectral geometry lies at the intersection of differential geometry, partial differential equations, and analysis. To a large extent it is motivated by questions originating in the study of real-life phenomena, such as vibration, heat propagation, oscilation of fluids, and quantum mechanical effects.

For example a model question, posed by Mark Kac half a century ago, is "Can one hear the shape of a drum?" The challenge is to understand the geometry of an idealized drum from the set of its vibration frequences, that is the Laplace eigenvalues. Kac’s question is closely linked to other topics in spectral geometry, including shape optimization, spectral asymptotics, and spectral invariants.

There are many starting points for a project in this general area, including isoperimetric inequalities, eigenvalue problems and spectral invariants in Riemannian geometry, eigenvalue problems in the minimal surface theory, and extremal eigenvalue problems.

Entry requirements

Applications are invited from candidates with or expecting a minimum of a UK first class honours degree or equivalent in Mathematics or a related subject. Applicant with a solid grounding in analysis and/or differential geometry would be well-suited to start working in any of these fields.

If English is not your first language, you must provide evidence that you meet the University’s minimum English Language requirements.

How to apply

Formal applications for research degree study should be made online through the university's website. Please state clearly in the research information section that the PhD you wish to be considered for is 'Spectral geometry' as well as Dr Gerasim Kokarev as your proposed supervisor.

We welcome scholarship applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates.  All scholarships will be awarded on the basis of merit.

If you require any further information please contact the Graduate School Office, e: maps.pgr.admissions@leeds.ac.uk.