An introduction to persistent homology

Title: An introduction to persistent homology

Venue: Webinar for DELTA (Descriptors of Energy Landscape by Topological Analysis

Abstract: This talk is an introduction to applied and computational topology, in particular as related to the study of energy landscapes arising in chemistry. We give a visual introduction to topology and homology groups. The focus of our talk is on persistent homology, which summarizes the changes in topological features across any increasing sequence of spaces. We emphasize sublevelset persistent homology, which provides a topological summary of real-valued functions, in particular energy functions. We also briefly introduce persistent homology applied to point cloud data, perhaps sampled from the low-energy conformations of a chemical system.

[Abacuscalcus]

Helpful intro, nice to see where this is being discussed in academia.

[andreasbeschorner]

Greetings. Any concepts for working with non metrizable topological spaces -- there are quite a lot of non pathological and non trivial ones and I imagine that, when interpreting data as topologies other than forming simplices, you might rather soon run into those.

[nrk]

I am most interested in the part you skipped that talked about one, two and three dimensional betti numbers and how to calculate it ? But overall it was informative. Thank You for the talk. :)

[nksupreme]

thanks for the talk. What software do you use to create the example about the sublevel filtration at 10:55?

[NoNTrvaL]

Please recommend some good books on this topic at the graduate level.

[vjysri]

Wow....is there a software or code I can use ?