My research interests focus in the mathematical modeling of biological systems and especially those which exhibit self-organization such as a shoal of fish or a flock of birds. Using asymptotic analysis, my work aims at connecting two levels of description of these systems: a microscopic description (particle dynamics) and a macroscopic description (PDEs). One of the many questions addressed by biological systems is to understand how local interactions among individuals lead to the formation of large structures. The derivation and analysis of macroscopic models give new insights to understand these phenomenons.

My research can be divided into three main axis:

• derivation of macroscopic models from microscopic dynamics,
• numerical and analytically study of the macroscopic models obtained,
• modeling of complex systems based on experimental data.

Software development

I develop several codes to implement large particle simulations and for the resolution of PDEs (written in Fortran or C). Data visualization (post-processing) is done using Paraview (VTK). Git repositories should be available soon.

Beside mathematics, I am also involved (in my free time) on the development of a smartphone app called Virtual plan 3D in partnership with the French company construireonline. The app allows to visualize a house plan in 3D using augmented reality.