Dr. Chad Higdon-Topaz
Macalester College
Date/ time: Thurs. Sept. 22nd, 2 – 3 PM
Location: SEH B1220
Hosted by: Prof. Megan Leftwich
Abstract
We demonstrate the utility of topological data analysis for understanding complex systems, using biological aggregations as a prototypical example. Biological aggregations are groups such as bird flocks, fish schools, and insect swarms in which organisms interact socially. These groups are striking examples of emergent self-organization, and simultaneously, they have served as inspiration for the development of algorithms in robotics, computer science, applied mathematics, and other fields. Aggregations give rise to massive amounts of data, for instance, the position and velocity of each group member at each moment in time during an observation or simulation. Interpreting this data to characterize the group's dynamics can be a challenge. To this end, we apply techniques of topological data analysis to the influential aggregation models of Vicsek et al. (1995) and D’Orsogna et al. (2006). We construe position and velocity data from numerical simulations as point clouds of data varying over time. Using a method called persistent homology, we identify topological features that persist over multiple spatial scales, and see that the topological analysis detects dynamical events that are invisible to more commonly used methods.
Biography
Professor of Mathematics Chad Topaz (A.B. Harvard, Ph.D. Northwestern) is an applied mathematician at Macalester College. His research on complex and nonlinear systems has been supported continuously by the National Science Foundation since 2006. A versatile investigator, Chad examines problems in biology, chemistry, physics, and the social sciences through several lenses, including data science, modeling, analysis, topology, geometric dynamical systems, numerical simulation, and experiment... all with an eye towards understanding and predicting complex behavior. Passionate about scientific communication and discourse, Chad has delivered over 100 talks at colleges, universities, and scientific meetings, and has co-organized numerous interdisciplinary minisymposia and workshops on chemical reaction diffusion systems, biological swarming, and related topics. His honors include a New Directions Research Professorship at the Institute for Mathematics and its Applications (the first given to a liberal arts college faculty member), a Kavli Frontiers Fellowship from the National Academy of Sciences, a Board of Trustees Award from Macalester College, and the 2013 Outstanding Paper Award of the Society for Industrial and Applied Mathematics, given to three publications selected from the pool of 16 SIAM journals over the prior three years.
Contact
The George Washington University, Mechanical and Aerospace Engineering
800 22nd St NW, suite 3000
Washington, DC 20052
[email protected]