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, I am interested in developing approaches for quantifying self-organization and robustly characterizing complex systems models and data.
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
- Data-driven modeling of complex social systems
- Forecasting U.S. elections using a dynamical-systems perspective
- Investigating social-movement dynamics on Twitter
- Agent-based modeling of pedestrian movement in lecture halls
- 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:
