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 classical results on reaction-diffusion problems, this lecture presented a series of recent developments on the Fisher-KPP equation, initially introduced in connection with the way a gene spreads in a population, on different types of propagation fronts, on branching Brownian motion and on a model of family trees in the absence or presence of selection.