Research overview:

Our broad research area is applied dynamical systems. I am interested in better understanding problems from diverse applications that involve individuals coming together to create rich, group-level dynamics. Examples of complex systems include cells in animal-skin patterns, voters in political elections, and pedestrians in crowded rooms. From an applied perspective, I develop predictive, experimentally testable models to help address empirical questions. The primary focus of my research in this direction is investigating pigment-cell dynamics in fish-skin patterns, with the goal of helping to identify links between genes, cell behavior, and visible animal characteristics. Alongside my work on fish patterns, complex social systems is a growing focus of my research program. From a mathematical perspective, because agent-based models are challenging to analyze, I am also interested in developing approaches for quantifying self-organization in collaborative projects.
Quick links to my research projects:
  • Modeling + analysis of cell dynamics in skin patterns
    • Modeling skin-pattern formation in fish
    • Topological data analysis of cell-based patterns
    • PDE modeling of cell dynamics with nonlocal interactions
    • Image analysis to describe pigment cells in vivo
    • Mechanistic modeling of pigment-cell communication
    • Identifying pattern transitions using TDA
  • Other projects in dynamical systems or math biology
    • Noise-induced tipping in periodically forced systems
    • Agent-based modeling of intracellular transport in neurons
    • Piecewise-deterministic Markov proccess perspectives on cell dynamics
    • Constructing networks from diary-based interaction data
    • Hybrid modeling of drug resistance and cancer development

Research gallery: