Research

I am an applied mathematician with interests in complex systems and mathematical biology. I use modeling, analysis, and computer simulation of differential equations systems to both provide insight and make predictions about biological and physical phenomena.

Pattern formation in complex systems We study the effect of connectivity between randomly behaving agents representing, e.g., fireflies flashing, neurons firing, and crowds applauding. Using a combination of numerical simulations and mathematical analysis, we investigate how the strength of interactions and the network of connections between the agents leads to a large variety of patterns and synchronization between the agents. This work has applications in biological systems, neuroscience and social sciences. Press: TCNJ Magazine, Winter 2020	Click here for more movies!
	Crawling cell motility We analyze a partial differential equations model of actin-propagated crawling cell motion. Using a combination of mathematical analysis and numerical simulations, we study parameter regimes of wherein cells can persistently move as well as the effects of patterned substrates on the motility of cells. Our work suggests mechanisms of cell sorting and directed cell motility of use to experimentalists.

Pattern formation in complex systems

We study the effect of connectivity between randomly behaving agents representing, e.g., fireflies flashing, neurons firing, and crowds applauding. Using a combination of numerical simulations and mathematical analysis, we investigate how the strength of interactions and the network of connections between the agents leads to a large variety of patterns and synchronization between the agents. This work has applications in biological systems, neuroscience and social sciences.

Press: TCNJ Magazine, Winter 2020

Click here for more movies!

Crawling cell motility

We analyze a partial differential equations model of actin-propagated crawling cell motion. Using a combination of mathematical analysis and numerical simulations, we study parameter regimes of wherein cells can persistently move as well as the effects of patterned substrates on the motility of cells. Our work suggests mechanisms of cell sorting and directed cell motility of use to experimentalists.