Mathematical models for the treatment of depressive disorders.
- New line to study the influence of biochemical and sociological factors on this type of disorders in collaboration with the biomedical sector.

Multiscale modeling and simulation of biofilms
- Developing descriptions of cellular aggregates such as baterial biofilms requires the study of mechanisms at the microcospic and macroscopic level as well as their interaction. Mathematical approaches for cell behavior often have a stochastic basis, informed by the dynamics of continuum variables (concentrations, flows...).
Describing the macroscopic responses of the cellular aggregate involves continuum models: 3D elasticity, plate and rod approximations, fluid transport in porous media, poroelasticity, interaction fluid/structure... Strategies to transfer key information between the microscopic and macroscopic submodels must be devised. Efficient simulation environments for the variety of equations in volved must be developed.

Long time behavior and perturbation methods in partial differential equations
- Recent angiogenesis models describe the dynamics of the vessel tip density through Fokker-Planck type equations with measure valued coefficients coupled to reaction-diffusion systems. Well posedness results, numerical schemes and long time dynamics are the subject of current research.

Variational methods for imaging
- Topological sensitivity based techniques have arisen as a powerful tool to reconstruct the geometry and properties of objects buried in a medium by scattering of electromagnetic, acoustic or thermal waves, without a priori knowledge on the objects. Applications to noninvasive imaging of biological and soft matter samples in digital holography settings at the nano and microscales are in progress.