Please note different day: Tuesday, April 14th.
Due largely to availability of software, current efforts in topological data analysis focus primarily on the use of persistence diagrams as a statistical invariant for distinguishing systems or behaviors. However, many scientific problems of interest would be more easily addressed by developing tools with more direct semantic connections to the structure of the data. Here, I will discuss two such efforts currently in development: the use of witness complexes and Dowker's theorem to study relationships between cycle representatives in related Vietoris Rips complexes, and the application of Chen's iterated integrals to the study of time series data. These projects are joint work with Iris Yoon and Darrick Lee, respectively.