Spectral Theory of Differential Operators

Outline

Research on this theme is characterised by a combination of functional and harmonic analysis with classical real and complex analysis, special functions and the asymptotic analysis of differential equations. Although the main emphasis is on developing the mathematical techniques, the operators studied are typically related to questions of theoretical physics; objects of current interest include Dirac operators, occurring in relativistic quantum mechanics and, without a mass term, in the description of the electronic properties of new materials such as graphene, as well as non-linear variants of the Schrödinger operator.

The questions to be studied concern the position and asymptotic distribution of eigenvalues as well as the properties of continuous spectral measures; in the case of the non-linear operators, even the definition and interpretation of such measures is an open question.

What is funded

Self-funded students only.

How to Apply

Applicants should submit an application for postgraduate study via the online application service http://www.cardiff.ac.uk/study/postgraduate/research/programmes/programme/mathematics

In the research proposal section of your application, please specify the project title and supervisors of this project and copy the project description in the text box provided.

In the funding section, please select the ’self -funding’ option.

We are interested in pursuing this project and welcome applications if you are self-funded or have funding from other sources, including government sponsorships or your employer.