I am interested in the study of dispersive PDEs, in particular boundary value problems and spectral properties of linear and integrable PDEs. In particular:
Boundary Values Problems
The Unified Transform method for linear PDEs
Spectral Theory
Spectral analysis of linear differential operators
Revivals, or the Talbot effect, for dispersive linear PDEs
Geophysical fluid dynamics
Optimal transport techniques for the analysis of models for large-scale atmospheric flows
My results on the spectral structure of odd-order linear differential operators earned me an invitation to give the Olga Tausski-Todd prize lecture at ICIAM 2011.
My research has been funded by EPSRC with two grants (2011-14 and 2016-19). I was a Leverhulme Fellow in 2014-15 and 2023-24. I was also the co-Director of the Mathematics for Planet Earth Centre for Doctoral Training (2014-2016)
I supervised several PhD students at the University of Reading (UoR) and at the Maxwell Institute ( HW-UoE):
D. Chilton, PhD, 2006 (UoR)
D.A. Smith, PhD 2011 (UoR)
D.K. Gilbert, PhD 2013 (UoR)
Stefania Lisai, PhD 2019 (HW-UoE)
Charlie Egan, PhD 2022 (HW-UoE)
George Farmakis, PhD 2022 (HW-UoE)
Théo Lavier, PhD expected 2025 (HW-UoE)