Research interests
A main topic of my research is studying wave propagation using differential geometry with focus on propagation of electromagnetic waves. One difficulty in this work is how to geometrically model the polarisation of the wave. Namely, due to the vectorial nature the electromagnetic field, the field can be polarised in different ways, and different polarisations can in general have different propagation properties. One approach to this problem I have studied is to model polarisation using contact geometry, which is a differential geometry where the fundamental quantity has a constantly rotating behaviour due to a non-integrability condition. In addition, I work on Gaussian beams (asymptotic solutions that behave as propagating wave packets) and sprays (the geometric theory of second order ODEs).
A motivation for my research is the inverse problem of travel-time tomography.