I am a lecturer/regional academic (staff tutor) in the Applied Mathematics group in the School of Mathematics and Statistics, where I contribute to teaching as part of module teams, carry out research, supervise PhD students and manage associate lecturers.
I was at the University of Southampton before joining the OU, where I specialised in mathematical modelling and numerical simulations, first as a PhD student in Physics and Astronomy, and then as a postdoctoral researcher at the Institute for Sound and Vibration Research (ISVR). This followed on from my MMath at the University of Bath.
My primary research interest is in optimising superoscillatory functions, which have wide and groundbreaking applications. Superoscillation is the phenomenon where a bandlimited function oscillates faster than its fastest Fourier component. An example of its application 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 to the achievable resolution. This opens up the possibility of taking much more detailed images of the microscopic world, for example of details within human cells.
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 numerical simulations and optimisation, including work on genetic algorithms, semi-analytic techniques and finite element methods.
See my personal website for more detail.
I am currently involved in the following modules: M373 (Optimisation) (I am module team chair), MS327 (Deterministic and Stochastic Dynamics), a new final year 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).
Encouraging student participation in mathematical activities in synchronous online tuition (2021)
Rogers, Katrine Sharp; Thomas, Claudi and Holmes, Hilary
Open Learning: The Journal of Open, Distance and eLearning ((Early Access))
Realising superoscillations: A review of mathematical tools and their application (2020-10)
Rogers, Katrine S. and Rogers, Edward T. F.
Journal of Physics: Photonics, 2, Article 42004(4)
Far-field Unlabelled Super-Resolution Imaging with Superoscillatory Illumination (2020)
Rogers, Edward T. F.; Quraishe, Shmma; Rogers, Katrine S,; Newman, Tracey A.; Smith, Peter J. S. and Zheludev, Nikolay I.
APL Photonics, Article 66107(5)
Far-Field Superoscillatory Metamaterial Superlens (2019-06-07)
Yuan, Guanghui; Rogers, Katrine S.; Rogers, Edward T. F. and Zheludev, Nikolay I.
Physical Review Applied, 11, Article 64016
Optimising superoscillatory spots for far-field super-resolution imaging (2018-04-02)
Rogers, Katrine S.; Bourdakos, Konstantinos N.; Yuan, Guang Hui; Mahajan, Sumeet and Rogers, Edward T. F.
Optics Express, 26(7) (pp. 8095-8112)