Topological Time Series Analysis for Hurricanes and Dynamical Systems

Explore the applications of Topological Data Analysis (TDA) in studying time series data through this informative 56-minute lecture. Delve into the world of algebraic topology and discover how persistent homology, a popular TDA tool, can be used to quantify the shape of data in a concise and robust manner. Learn about two specific applications: analyzing satellite imagery of hurricanes using persistent homology and investigating bifurcations in dynamical systems with zigzag persistence. Gain insights into how these topological methods can detect changing shapes over time and quantify features such as periodicity in complex datasets.