I am currently in post doctoral position in the Madynes team at LORIA.
Research topicsHere are some of my main subjects of interest:
- I'm interested in Crump-mode-Jagers processes which are known to be a very general class of branching processes with discrete state space. One of my main subject of interest on these objects are their behavior in long time and their applications in populations genetics.
- In the field of adaptitive dynamics, I am interested in the small mutation asymptotic of the so-called parabolic or integral Lokta-Volterra PDE. The solutions are known to concentrate as Dirac masses in the small mutation asymptotics. Under some conditions, the dynamic of these Dirac masses is known to stastify a constrained Hamilton-Jacobi equation. Nevertheless, understanding this dynamics (in particular in terms of the ressources) is a challenging issue. Results on these equation are usually obtain through analytic methods. My interest is to use probablistic methods to obtain new informations.
- Statistics for tree structured datas: Many data are naturally modelled by an ordered tree structure. The statistical analysis of a dataset of hierarchical records is thus of a great interest. In particular, detecting differences in large tree structures is a complex and challenging issue. In a recent work, we proposed to tackle this problem using contour processes of the considered trees. In particular, I am interested in the statistical analysis of conditioned Galton-Watson trees.
- Stochastic control in software defined networking: In the Madynes team, I'm a working on probabilistic methods in order to mitigate DDos attacks in the context of software defined networking