One main focus of my research is on probabilistic models and related statistical methods with applications in the sciences. In particular, I am interested in models that require mathematical and probabilistic formulation to characterize biological mechanisms. A few recent topics I have worked on with my colleagues are: formulation of probabilistic models and simulations to characterize the inheritance mechanism for a non-Mendelian species, construction of a mathematical procedure based on graph theory for life cycle analysis in population biology, and formulation and analysis of population structure in fishery and ecology.
As for the theoretical aspect, I have been involved in studying analytic properties of differential equations, in particular those related to uniqueness of solutions and characteristics of harmonic functions which have an important role in probability theory. Another research interest of mine is quantum statistical inference and potential applications of non-commutative probability.