Stochastic waves on metric graphs and their genealogies

Stochastic reaction-diffusion equations are important models in mathematics and in applied sciences such as spatial population genetics and ecology. These equations arise as the scaling limit of discrete systems such as interacting particle models, and are robust against model perturbation. In this talk, I will discuss methods to compute the probability of extinction, the quasi-stationary distribution, the asymptotic speed and other long-time behaviors for stochastic reaction-diffusion equations of Fisher-KPP type. Importantly, we consider these equations on general metric graphs that flexibly parametrize the underlying space. This enables us to not only bypass the ill-posedness issue of these equations in higher dimensions, but also assess the impact of space and stochasticity on the coexistence and the genealogies of interacting populations.