Reaction-diffusion problems : from front dynamics to genealogies

Reaction-diffusion models appear in a wide variety of fields, from mathematics to chemistry, from biology to sociology. It's remarkable that the same equations and models can be used in such a wide variety of contexts.
After recalling a few classic results, this lecture will present a series of recent developments on the Fisher-KPP equation, originally introduced in connection with the way a gene spreads in a population, on different types of propagation fronts, on branching Brownian motion and on the modeling of gene trees in the absence or presence of selection.