My work has been supported by three NSF research grants, including a CAREER award, which will be active during the academic years 2021-2025. Below I give a brief description of some projects my group is tackling.
Analysis of movement mechanisms to overcome the Allee effect: The movement strategy that a populations uses can make a difference between persitence and extinction. We are studying how we can quantify what a good movement strategy is. Morevoer, we are determing what movement strategies can help a population overcome an Allee effect, if they are subject to it. Our group is also looking at extending these ideas to systems in economics. In particular, we are developing a mathematical framework that can help explain the spatial formations of industrial clusters.
Territory formation in ecology: We are working on developing techniques to infer movement factors for social ecological species using non-local PDE models. Many animals have memory and use non-local information to decide how to move, thus, non-local partial differential equations are suitable.
Gentrification: We are developing models to understand the leading factors that lead to gentrification. Meta-population models can help us understand the spatial dynamics of wealth.
Dynamics of Violence: We are deloping multi-scale models to mathematize conceptual models for violence put forth by criminologists. This will be done from a public health lens.
Modeling Social Outburst: We have developed models to understand the dynamics of social outburts, such as rioting activity. These models consist of a social tension field and a level of activity. Our current focus is on trying to figure out a way to measure the social tension in real-life in order to predict possible shocks to the system.