Dr Katrine Rogers

Professional biography

My research interests are in mathematical and numerical modelling, including optimisation. I am currently working on optimising superoscillations for optical imaging and applications more generally. Superoscillation is the phenomenon where a band-limited function oscillates faster than its fastest Fourier component, and it has significant physical implications. One example is in taking images using optical instruments: it was previously thought that the resolution we can achieve in such images was fundamentally limited, but with superoscillations there is, in principle, no limit on the achievable resolution.

My previous research has included mathematical modelling of a range of applications, from modelling wave propagation in structural engineering to modelling electron and photon interactions in the vicinity of black holes. A recurring theme is novel approaches to the numeric solution of differential equations, with work on finite element methods, genetic algorithms, semi-analytic techniques and Fourier theory.

I am currently involved in the following modules: M373 (Optimisation) (I am module team chair), MS327 (Deterministic and Stochastic Dynamics), M374 (new module) and MST224 (Mathematical Methods).

My main collaborators are Dr E.T.F. Rogers (Optoelectronics Research Centre and Institute for Life Sciences, University of Southampton), Dr K.N. Bourdakos (Institute for Life Sciences and Department of Chemistry, University of Southampton) and G.H. Yuan (Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore).