Title: Applications of Topological Time Series Analysis to Hurricanes and Dynamical Systems
Abstract: Topological data analysis (TDA) is a fairly new 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 applications to time series data, detecting shape that changes over time and quantifying features like periodicity. In this talk, I will present two applications using tools from TDA to study time series data: the first using persistent homology to study satellite imagery of hurricanes and the second using zigzag persistence, a generalization of persistent homology, to study bifurcations in dynamical systems.