Most mathematical models introduced in the life and social sciences literature that describe inherently spatial phenomena of interacting populations consist of systems of ordinary differential equations, thus leaving out any spatial structure. The spatial component, however, is identified as an important factor in how communities are shaped, and spatial models can result in predictions that differ from their nonspatial counterparts. The aim of my research is to understand the role of space in ecology, epidemiology, population genetics, opinion dynamics, cultural dynamics and evolutionary game theory through the mathematical analysis of a class of stochastic processes known as interacting particle systems. These processes are ideally suited to investigate the consequences of the inclusion of a spatial structure in the form of stochastic and local interactions. This includes generalizations of the contact process and the voter model in spatially heterogeneous environments but also on inhomogeneous graphs, hypergraphs, and dynamic graphs.
