Scientific interests

I am interested in the mathematical modeling of complex biological systems, more particulary in the phenomena of emergence and self-organization, i.e the spontaneous formation of spatio-temporal structures at the population level, as a result of simple local interactions between individual agents. My works have various biological applications/targets, such as tissue morphogenesis, repair and decline, vasculogenesis, tumor growth, cell migration and others. My research has two complementary aspects: The first is pure mathematical modelling, i.e the building of mathematical models that are able to reproduce qualitatively (or better) quantitatively experimental data. This aspect involves strong interdisciplinarity and is made in close collaboration with experts from different fields (mainly biologists/physicists). When successful, our models enable to give insights into the key mechanisms at play in the systems of interest, and can have important impact on our understanding of complex biological systems that are not easily accessible by experiments. The other aspect of my research is devoted to the exploration of the link between different modelling scales, by using a multiscale approach combining the use of microscopic (agent-based) models with mesoscopic (kinetic) and macroscopic (fluid) models. This more theoretical aspect aims to help macroscopic models gain in predictive character by linking them as rigorously as possible to their microscopic counterpart.

Mathematical interests

  • Micro-macro passage from particle-based to macroscopic models

  • Kinetic theory

  • PDE analysis

  • Numerical methods: (AP-schemes, Minimisation algorithms, Finite Element methods, discretisation of stochastic processes ..)

Others

  • Development of Image processing codes