My research interests lie in the application of mathematical techniques from dynamical systems and PDEs to the study of phenomena arising in applied fields such as biology, ecology, material science, and engineering. The heart of my research is inter-disciplinary – not only in investigating models that come from other fields, but in collaborating with, learning from and contributing my own viewpoints to the people who are at the forefront of them.
Some of my significant achievements are:
- I was a part of a multi-disciplinary team that created and analyzed a new ecological model, and its associated reaction-diffusion-ODE system. The novelty of this model lays in the inclusion, for the first time, of interactions with the so-called toxicity produced by the decomposing biomass in the system. Our investigation uncovered new ecological phenomena that were, to date, undetectable in other classical models.
- Using techniques from the field of Geometric Singular Perturbation Theory (GSPT), I have analyzed a singularly perturbed, non-convex variational problem related to the formation of microstructures in material science. Combining geometric and numerical methods, I have obtained further insights into the structure of periodic, multi-scale solutions. to this minimisation problem.
- I have investigated a regularized model for Micro-Electro-Mechanical Systems (MEMS) by applying methods from dynamical systems and GSPT, in particular the desingularization technique known as blow-up. Our cutting-edge analysis allowed us to achieve a precise description of steady-state solutions and a detailed resolution of the resulting bifurcation diagram.
- I have significantly contributed to an analytical study concerning long-time behaviour of solutions for a non-local Cahn-Hilliard equation with singular potential, degenerate mobility, and a reaction term. This study has been particularly crucial, not only because it provides insights on the evolution of the system, but also because it offers great support in numerical analysis.