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Spectral Theory of Differential Operators

  • Full or part time
  • Application Deadline
    Applications accepted all year round
  • Self-Funded PhD Students Only
    Self-Funded PhD Students Only

Project Description

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.

References

Applicants should submit an application for postgraduate study via the online application service

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.

Related Subjects

How good is research at Cardiff University in Mathematical Sciences?

FTE Category A staff submitted: 24.05

Research output data provided by the Research Excellence Framework (REF)

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