Professor Topaz is an applied mathematician working in dynamical systems and modeling, with a focus on patterns in nature (especially biological swarms). His research program focuses on the modeling, computation, and analysis of nonlinear systems and is particularly interested in natural systems that spontaneously self-organize or form patterns. Prof. Topaz’s National Science Foundation supported research program is centered on collaboration with students in the XMAC Lab (eXperiment, Modeling, Analysis, and Computation). EDUCATION: AB Harvard College; MS and PhD Northwestern University. Professor Topaz has been teaching at Macalester since 2007.
Flipped Calculus: A Study of Student Performance and Perceptions (with Lori Beth Ziegelmeier), PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies (2015)
Topological data analysis of biological aggregation models (with Lori Ziegelmeier and Tom Halverson), PLoS One (2015)
We apply tools from topological data analysis to two mathematical models inspired by biological aggregations...
Social Aggregation in Pea Aphids: Experiment and Random Walk Modeling (with Christa Nilsen, John Paige, Olivia Warner, Benjamin Mayhew, Ryan Sutley, Mathew Lam, and Andrew J. Bernoff), PLOS One (2013)
Nonlocal aggregation equations: A primer of swarm equilibria (with Andrew J. Bernoff), SIAM Review (2013)
Locust dynamics: Behavioral phase change and swarming (with Maria R. D'Orsogna, Leah Edelstein-Keshet, and Andrew J. Bernoff), PLoS Computational Biology (2012)
Locusts exhibit two interconvertible behavioral phases, solitarious and gregarious. While solitarious individuals are repelled from...
Contributions to Books
Fractional bandwidth reacquisition algorithms for VSW-MCM (with Ben Cook, Daniel Marthaler, Andrea L. Bertozzi, and Mathieu Kemp), Multi-robot systems: From swarms to intelligent automata (2003)
Autonomous underwater vehicles are gradually being recognized as key assets in future combat systems. Central...
This dissertation investigates pattern selection in two-frequency forced Faraday waves. In this system, a fluid...