My area of research expertise can be broadly characterised as the analysis of partial differential equations (PDEs) and spectral theory. This covers a wide range of research topics from the very applied (elasticity, shell theory, hydroelasticity, trapped modes) to the very pure (microlocal analysis, symplectic geometry, Tauberian theorems, fractal drums).

I am currently interested in the study of systems of hyperbolic PDEs using  microlocal techniques. These techniques allow one to construct explicitly, modulo smooth terms, solutions in the form of wave packets. Here the key word is Fourier integral operator as it gives a rigorous mathematical meaning to the term `wave packet'. My interest in systems of hyperbolic PDEs is fuelled by the observation that application of microlocal techniques leads to the natural emergence of geometric concepts such as metric, connection, torsion, spinor, Dirac Lagrangian, electromagnetic covector potential etc. My hope is that in the long run this analysis could be developed to give a new mathematical description of fermions (elementary particles such as the neutrino or the electron), one in which geometry arises as a result of solving PDEs rather than being introduced axiomatically.