This event is in-person and open only to Princeton University ID holders

A longstanding challenge in ecology, and many other natural sciences, is to bridge the gap between detailed microscale descriptions of systems and more tractable models of their macroscale behavior. Mean-field limits of interacting particle systems are a popular method to connect models at different scales; in this talk, we discuss their application to spatially extended models in vegetation and population dynamics. Our first application generalizes a non-spatial model of forest-savanna dynamics and allows us to understand how long-run transient dynamics and heterogeneity-driven “front-pinned solutions” arise. Our second application is a “toy” opinion dynamics model with diffusive and jump-type movement. This example illustrates how the mean-field limiting procedure can generate simple phenomenological models of complex collective behavior. We only assume a basic knowledge of probability and dynamical systems, and the talk will be suitable for those broadly interested in mathematical modeling in applications.