# The Effect of Diffusion on a Line on Fisher-KPP Propagation

*By Henri Berestycki, EHESS, Paris*

I will present a system of equations describing the effect of including a line (the "road") with a specific diffusion on biological invasions in the plane. Outside of the road, the propagation is of the classical Fisher-KPP type. We find that past a certain precise threshold for the ratio of diffusivity coefficients, the presence of the road enhances the speed of global propagation. One can determine the asymptotic shape of propagation in every direction influenced by the road. I will discuss several further effects such as transport, reaction on the road or the influence of various parameters. I will also describe some variants of this system. I report here on results from a series of joint works with Jean-Michel Roquejoffre and Luca Rossi.