Persistent homology is a tool from topological data analysis which describes the multi-scale topology of data sets. The resulting output is a persistence diagram, which can be viewed as a measure supported on the upper half plane. For time-varying data, we can compute a persistence diagram at every time point, and obtain a path of persistence diagrams describing the temporally evolving topology of the data. In this talk, we explore both the theoretical and computational aspects of using path signatures to study such paths and discuss connections with optimal transport along the way. This is joint work with Chad Giusti.
Darrick is a PhD student in the Applied Mathematics and Computational Sciences program at the University of Pennsylvania working under Prof. Rob Ghrist. For more information, see Darrick's webpage.