Here are some projects I am currently invilved in.
Analysis of relocation mechanisms to overcome the Allee effect: How populations relocate can make a difference between persitence and extinction. We are working in analyzing the best relocation mechanisms to overcome an Allee effect. Our group is also looking at extending these ideas to systems in economics.
Territory formation in ecology: We are working on developing techniques to infer movement factors for social ecological species using non-local PDE models.
Gentrification: We are developing models to understand the leading factors that lead to gentrification.
Dynamics of Violence: We are deloping multi-scale models to mathematize conceptual models for violence put forth by criminologists.
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.