Research Projects
My work has been supported by three NSF research grants, including a CAREER award, which will be active during theÌýacademic years 2021-2025.Ìý Below I give a brief description of some projects my group is tackling.ÌýÌýÌý
Analysis of movement mechanisms to overcome the Allee effect:Ìý The movement strategy that a populations uses can makeÌýa difference between persitence andÌýextinction.Ìý We are studying how we can quantify what a goodÌýmovement strategy is.Ìý Morevoer,Ìýwe are determing what movement strategies can help a population overcome an Allee effect, if they are subject to it.ÌýÌýOur group is also looking at extending these ideas to systems in economics.Ìý In particular, we are developing a mathematical framework that can help explain the spatial formations of industrial clusters.ÌýÌý
Territory formation in ecology:ÌýWe are working on developing techniques to infer movement factors for social ecological species using non-local PDE models.Ìý Many animals have memory and use non-local information to decide how to move, thus, non-local partial differential equations are suitable.ÌýÌý
³Ò±ð²Ô³Ù°ù¾±´Ú¾±³¦²¹³Ù¾±´Ç²Ô:ÌýWe are developing models to understand the leading factors that lead to gentrification.Ìý Meta-population models can help us understand the spatial dynamics of wealth.Ìý ÌýÌý
Dynamics of Violence:ÌýWe are deloping multi-scale models to mathematize conceptual models for violence put forth by criminologists.Ìý This will be done from a public health lens.ÌýÌý
Modeling Social Outburst:ÌýWe have developed models to understand the dynamics of social outburts, such as rioting activity.Ìý These models consist of a social tension field and a level of activity.Ìý 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.
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