Applications of topological data analysis to temporal and spatial data

Topological Data Analysis (TDA) is a field with tools to quantify the shape of data in a manner that is concise and robust using concepts from algebraic topology. Persistent homology, one of the most popular tools in TDA, has proven useful in many different fields. However, zigzag persistence and multi-parameter persistence have seen far fewer applications. In this talk I’ll present two applications of TDA using these generalizations of persistent homology. First, I’ll discuss using zigzag persistence to analyze data that arises from dynamical systems. Second, I’ll introduce some preliminary results on a case study analyzing access to public resources using techniques inspired by multi-parameter persistence.