Research Fellow in Mathematical Analysis

Do you have an established background in analysis of partial differential equations, spectral theory, or rigorous numerical analysis?

Do you want to further your career in one of the UK’s leading research intensive universities?

We are looking for a postdoctoral Research Fellow to work on our Leverhulme funded research project, Mathematical Analysis of Casimir Interactions. Casimir interactions between conducting materials can be understood as being induced by vacuum energy fluctuations of the electromagnetic field. T

he computation of Casimir forces between objects relies heavily on local spectral data that is derived from the spectral decomposition of the Laplace operator. These are connected via the Fourier and the Mellin transform to the local heat kernel and the local wave trace.

You will contribute to our project aim, which is the full mathematically rigorous analysis of these local spectral quantities. This will include asymptotic expansions with rigorous error estimates, representation formulae using scattering theory and perturbation theory. One of the applications of such an analysis is to make Casimir force computations rigorous and numerically stable. In a second stage of the project, you will be involved in seeking to implement stable numerical procedures for the computation of Casimir interactions in the existing softwage package BEM++, working in collaboration with the Co-Principal Investigator of the project, Dr Timo Betcke at UCL. This part of the project is interdisciplinary, and you will engage with aspects of numerical analysis.

You will have a PhD in Mathematics or a closely allied discipline, together with knowledge of analysis, spectral theory, spectral geometry, or rigorous numerical analysis, although knowledge of rigorous quantum field theory is not required.  You will have a willingness to engage in inter- and intra-disciplinary research, working both independently and with a larger team of researchers.  

To explore the post further or for any queries you may have, please contact: Professor Alexander Strohmaier, Chair in Analysis, Tel: +44 (0)113 343 8884, Email: a.strohmaier@leeds.ac.uk