Lunch will be served at 11:45 AM.
Recent developments in shape representation and comparison call for the use of topological descriptors. In this talk, we are interested in how to represent shapes embedded in R^d. In particular, the descriptors of interest are the persistence diagram, the Euler characteristic function, the Betti function, and their verbose counterparts. We provide some experimental studies demonstrating the gap between theory and practice in how many descriptors are needed to achieve data analysis tasks. Motivated by this, we investigate these six common topological descriptors, studying how many of each type of descriptor are needed to represent a shape. Building from this knowledge, we establish a framework that allows for a quantitative comparison of topological descriptors.
Brittany Terese Fasy is an Associate Professor at Montana State University, with a primary appointment in the School of Computing and an affiliate position in the Department of Mathematical Sciences. Before being a faculty member at MSU, she earned her PhD from Duke University and worked as a postdoc at both Carnegie Mellon University and Tulane University. Her research is in computational topology and statistical approaches to topological data analysis. Her work explores problems such as data on graphs, defining invariants for directed topological spaces, algorithms for topological data analysis, and the mathematical stability of topological and geometric shape descriptors. Her research is grounded in real-world applications, including road network analysis and prostate cancer prognosis. In addition to her work in computational topology, she leads a project on bringing CS to rural and tribal communities throughout Montana.