Speaker
Description
In recent years, the qualitative study of models derived from neuroscience has experienced significant progresses, particularly within the communities of probabilist and PDE specialists. The aim is to use certain models to understand the emergence of complex dynamics observed within interacting neural networks.
In this regard, numerous PDE models have been proposed, presenting structures, and therefore mathematical difficulties, that vary greatly depending on the modeling choices made. We will begin with an overview of the main issues and existing results for PDE models derived from neuroscience that are now relatively well understood, in both linear and non-linear regimes. We will then focus on a particular framework where modeling involves equations with degenerate diffusion, for which, even in the simplest (linear) case, several questions remain open.
