Starting with a few motivating examples, I will sketch some basic ideas related to the analysis of structural and functional data via the technique persistent homology. This will include the formulation of 1D persistent homology, its representation through barcodes and persistence diagrams, as well as some foundational results. Time permitting, I also will discuss recent advances that expand the original concept of 1D persistence modules, leading up to new variants of 1D persistent homology whose barcodes and persistence diagrams enrich the geometric information about the shape of data captured through topological data analysis.
This is a joint Math Department-ICM Colloquium lecture.
Washington Mio earned his doctoral degree in mathematics from the Courant Institute of Mathematical Sciences, New York University. Before joining the Mathematics Department at Florida State University, where he currently is professor and chair, he was a member of IMPA in Brazil and also held visiting appointments at the Courant Institute and Cornell University. His research interests are in geometric topology, geometric and topological data analysis, and applications. In 2015, he became a Fellow of the American Mathematical Society.