Codes and Expansions (CodEx) Seminar

Elizabeth Munch (Michigan State University):
Comparing Embedded Shapes Using Topological Summaries

The goal of the field of topological data analysis (TDA) is to quantitatively encode and measure shape using Algebraic Topology. The available tools encompass both algebraic constructions (such as persistence diagrams and Euler characteristics) as well as graph based representations (such as Reeb graphs, mapper graphs, and merge trees). Applications of TDA have exploded in recent years, finding use in a diverse array of domains including plant biology, neuroscience, mechanical engineering, and many more. This increased interest is due to its now extensive theoretical foundation, and more recently due to the increased availability of more efficient algorithms and software making TDA pipelines more readily accessible to domain scientists. In this talk, we will review some of the tools available with a particular focus on encoding embedded shapes in \(\mathbb{R}^d\) (with most of our applications living in the setting of \(d=2,3\)), and for creating metrics between these representations to allow for access to tools such as statistics and machine learning.

This is a joint work with Ji Shi.