I am working in mathematical biology. I have listed below some current and past research activities. Please, visit the Publications page for a complete list of papers.

Research topics

  • Mesoscopic models in biology: We aim to develop mathematical tools to analyse models with a multiscale/multivariate structure. This includes chemotactic waves of swimming bacteria E. coli, reaction-transport equations, dispersal evolution during species invasion, maladaptation in age-structured populations, anomalous diffusion. This is the purpose of the ERC starting grant MESOPROBIO (2015-2020).
  • Optimal control and ergodicity: together with Pierre Gabriel (INRIA Lyon) we have recently proved an ergodicity result for a class of problems arising in optimal control, where the Hamiltonian is far from being coercive. This work is motivated by applications to PMCA protocol optimization.
  • Front propagation and kinetic equations: in collaboration with Emeric Bouin (ENS de Lyon) and Grégoire Nadin (Paris 6) we have investigated the existence and stability of hyperbolic traveling waves with a source term (accounting for growth of individuals). Together with Emeric Bouin we have derived a new eikonal equation, following the WKB ansatz for a linear kinetic transport equation with a BGK scattering operator.
  • Spontaneous cell polarization: the ANR project MODPOL is dedicated to this issue. This project involves Thomas Lepoutre (INRIA, Lyon), Nicolas Meunier (Paris 5), Matthieu Piel (Institut Curie, Paris), Paul Vigneaux (ENS de Lyon) and Raphaël Voiturier (Paris 6).
  • Kinetic equations for chemotaxis: in collaboration with Jonathan Saragosti, Axel Buguin and Pascal Silberzan (Institut Curie, Paris), Nikolaos Bournaveas (University of Edinburgh) and Benoît Perthame (Paris 6), we have shown that kinetic models are well adapted to describing collective bacterial motion for E. coli swimmers. We have also studied the possible behaviours of kinetic models for chemotaxis (global existence using dispersion and Strichartz estimates, blow-up).
  • Analysis of the Keller-Segel model: global existence via energy methods, blow-up. My collaborators on this subject are Adrien Blanchet (Université de Toulouse), José Antonio Carrillo (UAB, Barcelona), Lucilla Corrias (Université d'Evry val d'Essonne), Mohamed Aberrahman Ebde (Université Paris 13), and Benoît Perthame (Paris 6).
  • Modelling of neuro-degenerative diseases: analysis of polymerization-fragmentation equations for prion diseases (coll. Marie Doumic, Pierre Gabriel, Natacha Lenuzza, Franck Mouthon, Benoît Perthame); modeling of Balo concentric sclerosis (with Roman H. Khonsari).