Research Fellow at the Korea Institute for Advanced Study
I am a mathematician specialising in Dynamical Systems. My research is centred around the theory of Dynamical Systems, focusing on its applications in nonlinear mathematical models — ordinary differential equations (ODEs) and partial differential equations (PDEs) — that arise in physics and other areas of science. In particular, I am interested in understanding how these systems exhibit qualitative changes when parameters are varied; especially, when these changes emerge as a consequence of intersections between global objects, such as stable and unstable manifolds associated with saddle equilibria and periodic solutions. When these intersections occurs, one refers to them as global bifurcations, and they are the organising centres for creating periodic solutions, exotic behaviour and chaos in nonlinear dynamics.
My research interests have brought me to work alongside theoretical and experimental physicist in different optical models that describe state-of-the-art devices, e.g., photonic crystal nanocavities and optical fibres (see my publications). I am also interested in biological applications; in particular, in the dynamics of species abundance and extinction in ecological networks when the interaction matrix between species has structured or is random
My current position is Research Fellow in the School of Computational Sciences at the Korea Institute for Advanced Studies.
For a comprehensive list of my peer-review publications, and arXiv drafts of submitted manuscripts