I have always been fascinated with the mathematical underpinnings of reality. Recently, the focus of my research lies in non-linear PDEs and non-convex calculus of variations. Particularly, I am interested in rigorous mathematical models for phase transformations in solid crystals.
One such model is the Ball-James model for martensitic phase transformations which is based on energy minimisation. This model stands alongside many non-rigorous phenomenological theories that are missing a fundamental underlying principle, and thus are unable to decide whether the conclusions deviate from observation due to problems in the modelling or due to shortcomings in the experimental set-up.
By pursuing a mathematical approach one is often able to go beyond the description of observed features and create a predictive theory. This in turn opens up doors to creating materials with new and exceptional properties.