My research mainly focuses on the development, the mathematical analysis and the numerical simulation of spatio-temporal models in population dynamics and population genetics: partial differential equations (PDE) and integro-differential equations. My main goals are to understand range expansion or range shift phenomenon as well as the role of endogeneous and exogeneous factor on the diversity of a expanding population. More precisely, here is a list of research topics I am interested in
- Nonlinear partial differential equations and integro-differential eqautions;
- Traveling waves and spreading properties in homogeneous and heterogeneous media;
- Inside dynamics of traveling wave, transition wave and expanding solution of general parabolic equations;
- Inverse problems for parabolic equations with non-constant coefficients.
- Reaction-dispersion models in homogeneous and heterogeneous media;
- Population dynamics and population genetics. Mathematical studies of range expansions;
- Role of the Allee effect and of long distance dispersal events;
- Effect of climate change on genetic diversity of a population.