Primer on Persistent Homology and Persistent Diagrams

Mr. Joe Paulson
Graduate Teaching Assistant
University of Wisconsin – Milwaukee

Persistent diagrams are powerful mathematical tools used in the field of topological data analysis (TDA). These diagrams provide a concise and intuitive representation of topological features in data sets, particularly those that exhibit complex and multi-scale structures. Unlike traditional approaches, persistent diagrams capture the evolution of topological features across a range of spatial resolutions, allowing for the identification of robust and stable patterns amidst noise and variation.

In this talk, we explore the fundamental concepts behind persistent diagrams, such as persistence homology and barcode representations (No prior background will be assumed). In next week’s talk by Jillian Cervantes, we will see an application of persistent diagrams with time series data to explore gravitational wave data.