2016 REU Mini-Course – Topological Data Analysis and Persistent Homology

This page is for notes and materials for my mini-course on topological data analysis and persistent homology.

• Lecture 1 – Topological Data Analysis

Good surveys of persistent homology and its uses in geometry and data analysis include:

• Carlsson – Topology and Data (2009)
• Edelsbrunner, Harer – Survey of Persistent Homology (2008)
• Weinberger – What is persistent homology? (2011)
• Otter, Porter, Tillmann, Grindrod, and Harrington – A Roadmap for the Computation of Persistent Homology (2016)

A recent article on the use of persistent homology in studying flu strains is:

• Chen, Carlsson, Rabadan – Topology of Viral Evolution (2013)

Computer packages for implementing persistent homology computations include:

• Javaplex (requires MatLab or other Java based system)
• Perseus (requires C++ compiler)

Applied Topology is an online repository for conferences, software and article releases, and openings.