Beginning with an intuitive description of topology, I will describe the topological data analysis (TDA) pipeline, which maps data to summary objects such as Betti curves, merge trees, and persistence diagrams. This pipeline can be viewed as a sequence of maps between spaces, which are typically many-to-one. Studying the inverse problem for these maps yields interesting connections between data science, geometry, and combinatorics. I will describe one inverse problem in detail, which exemplifies how merge trees and the symmetric group combine to give a new summary statistic for neuroscience.

All are welcome to attend as this talk assumes no pre-requisites in topology or data science.