- Mathematical aspects of materials science: solid mechanics, fracture mechanics, atomistic modelling of fracture and other crystalline defects, near-crack-tip plasticity; including uncertainty quantification, numerical simulations and numerical analysis.
- Analysis of PDEs: gradient flows inspired by optimal transportation theory, with focus on unbalanced optimal transport (Hellinger–Kantorovich distance) and its entropic regularisation.
(1)Analysis of evolutionary partial differential equations: In my capacity as a Research Fellow at University of Birmingham, I am working with Dr Hong Duong on the analysis of a class of reaction-diffusion equations, cast as gradient flows with respect to metrics arising from optimal transportation theory. The particular focus is entropic regularisation of gradient flows related to unbalanced optimal transport (the Hellinger-Kantorovich distance).
(2)Atomistic-scale based modelling of fracture and related phenomena in crystalline materials: My main research interest concerns developing a mathematically rigorous theory of fracture starting from the atomistic scale, focusing on both brittle fracture and near-crack-tip plasticity.
(3)Uncertainty Quantification for interatomic potentials: I am also working on developing an information-theoretic stochastic approach to atomistic material modelling, based around the idea of invoking Maximum Entropy Principle to infer the prior probability distribution of parameters specifying the interatomic potential. The on-going work is aimed at generalising this framework to cover modern machine learning potentials, which typically have 100+ parameters.