Denis D. Patterson
*This event is * IN PERSON * (in-person is open only to Princeton University ID holders)
Spatial stochastic mean-field models and applications
Abstract: 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.
Bio: Denis Patterson is an applied mathematician working on problems in mathematical biology using tools from probability, PDE, and dynamical systems theory. He completed his Ph.D. in Applied Mathematics on nonlinear functional differential equations at Dublin City University in 2018. He was a postdoctoral researcher in the Department of Mathematics at Brandeis University before joining the High Meadows Environmental Institute at Princeton, where he works with Prof. Simon Levin on models of tropical vegetation dynamics.