PhD Public Lecture - Luis Scoccola (Math)

Title: Locally persistent categories and metric properties of interleaving distances

Abstract: When estimating topological features of continuous objects from finite samples, one has to produce a topologically interesting object given a finite metric space. When showing that such a procedure is robust, one endows the collection of possible inputs and the collection of outputs with metrics, and shows that the procedure is continuous with respect to these metrics. Category theory has proven valuable when defining these procedures and metrics, and when proving that these procedures and metrics are well-behaved. I will present a notion of category specifically designed for these tasks, and I will discuss applications to Topological Data Analysis.