Introduction to Persistent Homology

This video gives an accessible introduction to persistent homology, which is a popular tool in topological data analysis and also a subject of my research.

Citations and links to papers referenced in this video:

Robert Ghrist, "Barcodes: The Persistent Topology of Data"

Herbert Edelsbrunner and John Harer, "Persistent Homology -- A Survey", in Twenty Years After, AMS (2007).

David Cohen-Steiner, Herbert Edelsbrunner, and John Harer, "Stability of Persistence Diagrams", in Discrete and Computational Geometry, vol. 37 (2007), p. 103-120.

Afra Zomorodian and Gunnar Carlsson, "Computing Persistent Homology", in Discrete and Computational Geometry, vol. 33 (2005), p. 249-274.

Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva, and Afra Zomorodian, "On the Local Behavior of Spaces of Natural Images", in International Journal of Computer Vision, vol. 76 (2008), p. 1-12.

Jose Perea and Gunnar Carlsson, "A Klein-Bottle-Based Dictionary for Texture Representation", in International Journal of Computer Vision, vol. 107 (2014), p. 75-97.

Jose Perea and John Harer, "Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis", in Foundations of Computational Mathematics, vol. 15 (2015), p. 799-838.

[diegosierracosta]

This is what teaching is about, it's incredible how you explained such a complex concept in a very understandable way. Thank you!

[foo_tube]

Please do more videos! You are good at this. I have no significant math background, but I understood all of this! We need more teachers like you who can reach us normies with advanced mathematics!

[robertschlesinger]

Excellent introductory video on persistent homology. Many thanks for the links to the relevant papers.

[loosecannon]

Just attended a lecture from Gunnar Carlsson on TDA which went way over my head. This video has cleared some things up!

[holographictheory]

Would absolutely love more videos! This was, hands down, the best video on TDA/persistent homology that I've ever seen

[resocios]

Thank you so much for this clear and motivating introduction to the topic!

[onzie]

It's been several years since I left academia and simplicial complexes behind, but TDA looks really interesting, and I'm so glad I watched this straight forward and informative video.

[srinovita]

This video is great! I'm currently doing my master thesis on persistent homology and your videos help me a lot to understand it! Thank you!

[vamanieperumal]

Excellent delivery of concepts! Thanks a lot!

[syifahah]

Oh my my so clearly explained! Short and robust! Thank you so much :D

[jinyunghong]

Thank you so much for your great introductory video!

[mambu]

wow as a math undergrad taking only pure subjects this sounds really cool

[abolfazltaghribi]

This video is abstract and clear about the notions. Thank you!

[AjayTalati]

Thank you for the very clear explanations - I think you're a really good teacher :)

[hangyin]

Simple and easy to understanding! Thank you!!!

[Jinsun]

Fantastic explanation, thank you. Top notch.

[davidwaller]

Thanks for the introduction. That's very interesting!

[aoweishen]

Praise for this really nice and clear video.
However, could you keep on making more videos, especially on the advances of this area? I am on the verge of choosing a topic in statistics, and some great professor said this is the future, but I don't know whether I can handle these stuff.

[jerryzhang]

Very understandable short video course.

[ИванИваныч-би]

very interesting and very well explained