Orateur
Description
Biological systems, such as living tissues, have been extensively studied through a wide variety of mathematical models, ranging from individual-based descriptions to continuum PDEs and free-boundary problems. Different scaling regimes and singular limits provide a way to connect these models, offering a more unified understanding of the underlying biological phenomena. In this course, we will explore how agent-based models can be linked to nonlocal PDEs through mean-field limits, how nonlocal PDEs can be related to local PDEs through localization limits, and how PDE models can give rise to free-boundary problems through incompressible limits. Throughout the course, we will emphasize the mathematical tools used to rigorously justify these transitions, including Wasserstein estimates, energy methods, and compactness arguments.