Explore topological data analysis through this comprehensive tutorial collection featuring 39 presentations from leading researchers and practitioners in applied algebraic topology. Learn fundamental concepts including persistent homology, barcodes and persistence diagrams, Čech and Vietoris-Rips complexes, and the Euler characteristic for measuring shape. Master practical tools and algorithms such as the persistence homology reduction algorithm, bottleneck distance computation, and Mapper for data visualization. Discover programming implementations in Python and Julia for TDA applications, including tutorials on Ripser++, Persim, and persistence image analysis. Examine advanced topics like Bregman persistence homology, multidimensional matching distance, sliding window persistence, and statistical hypothesis testing through TDA. Apply these techniques to real-world problems including professional basketball analytics, blood vessel image analysis, mosaic creation from images, and measuring dynamics of time-varying systems. Gain insights into theoretical foundations through discussions of the Niyogi-Smale-Weinberger theorem, discrete Morse theory, algebraic stability of persistence diagrams, and homeomorphisms versus homotopy equivalences.

Syllabus

Bregman persistence homology [Hana Dal Poz Kouřimská]
What is the difference between persistence barcodes and persistence diagrams? [Henry Adams]
Getting started with Python for TDA [Sarah Percival]
Intuition for Persistent Homology Reduction Algorithm [Teresa Heiss]
Measuring shape with the Euler characteristic [Erik Amézquita]
Finite Topology [Shelley Kandola]
Statistical hypothesis testing through TDA [Christian Hirsch]
The Niyogi-Smale-Weinberger Theorem & its relatives [Josué Tonelli Cueto]
An Application of TDA to Professional Basketball [Jerome Roehm]
The Bottleneck Distance [Danish Ali]
Introduction to Mapper [Ananthakrishna Gopal]
A Youtuber's guide to discrete Morse theory [Nick Scoville]
Merge Tree Representation for 0th Persistent Homology [Petar Hristov]
Machine Learning with Persistence Images [Nick Sale]
Intrinsic Persistent Homology [Ximena Fernández]
How to Create Mosaics from Images [Robin Belton]
Computing the Bottleneck Distance [Niklas Hellmer]
Algebraic Stability of Persistence Diagrams [Ziva Urbancic]
Čech, Vietoris-Rips, Delaunay and Alpha complexes [Francesca Tombari]
Let’s talk about random Cech and Vietoris-Rips complexes [Andrew M. Thomas]
Clear and compress for persistence algorithm [Barbara Giunti]
Multidimensional Matching Distance [Mehmet Ali Batan]
Intro to topological data analysis in Julia [Melinda Kleczynski]
Non-topological persistence [Massimo Ferri]
Voronoi diagram, Delaunay and Alpha complexes: A Visual Intro [Ondřej Draganov]
An Introduction to Topological Spaces [Lori Ziegelmeier]
Computing Persistence diagrams using Linear Algebra [Donald Woukeng Feudjio]
Persistence Curves [Austin Lawson]
The Shape of Data [Péguy Kem-Meka]
Persistent homology for blood vessel images [John Nardini]
(Intro to) Sliding Window Persistence [Hitesh Gakhar]
An introduction to Persim for analyzing persistence diagrams [Waqar Hussain Shah]
Homeomorphisms and Homotopy Equivalences [Henry Adams]
A Fun Intro to the Anti-Rips Complex [Brett Jefferson]
Crockers to Topologically Measure Dynamics of Time-varying Systems [Lori Ziegelmeier]
Kernels for Persistent Homology [René Corbet]
Persistence Images [Rachel Neville]
Tutorial on Ripser++ [Simon Zhang]
Mapper Tutorial - COIL-20 [Ahmed Abdelkader]