Persistent homology: working seminar


Schedule The seminar is now over. Thanks to everyone for their participation.

We met on Mondays, 4.10-5.00pm, in JCMB 4312.

  • Monday 21 January: Tom Leinster, Overview.
  • Monday 28 January: Emily Roff, The Cech and Rips complexes.
  • Monday 4 February: Sjoerd Beentjes, Barcodes and the structure theorem
  • Monday 11 February: Henry-Louis de Kergolay, Stability
  • Monday 18 February: no seminar (Carnival of Creative Learning)
  • Monday 25 February: Henry-Louis de Kergolay, More on stability
  • Monday 4 March: Double bill: (1) Henry-Louis de Kergolay, End of the proof of the stability theorem; (2) Tom Leinster, Categorical approach(es) to stability (illegible notes)
  • Monday 11 March: Johan Martens, Morse theory and persistent topology

Resources   This is a pretty random list, and definitely not intended to dictate the direction of the seminar. I just wanted to gather together some of the resources I've stumbled across or had recommended to me.

Please tell me about any other papers/books you've found useful, and I'll add them here.

Surveys, tutorials, and expository

  • Robert Ghrist, Barcodes: the persistent topology of data. The plan is to use this as our main reference and our guide.
  • Robert Ghrist, Elementary Applied Topology. This is a unique and very browsable book filled with interesting vignettes. You can download chapters from the link, or buy the whole thing (it's cheap!). Section 5.13 is about persistent homology.
  • Michael Lesnick, Studying the shape of data using topology. Two-page expository article for the newsletter of the Institute for Advanced Study. Among other things, it explains in brief the story of how topological data analysis uncovered a previously unknown subtype of breast cancer.
  • Gunnar Carlsson, Topology and data. Carlsson has made pivotal contributions to applied topology (and pure topology, for that matter). This is an earlyish survey paper in the Bulletin of the AMS. (Yes, 2009 counts as "early" in this subject.)
  • Pawel Dłotko, Computational and applied topology, tutorial. Chapter 7 is about persistent homology.

Geometric foundations

Connections with algebra

  • Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot, The structure and stability of persistence modules. I had the first two sections recommended to me, but I haven't looked into them yet. Gets into some stuff about representations of quivers! Also has some sophisticated stuff on stability (more on which below).
  • Afra Zomorodian and Gunnar Carlsson, Computing persistent homology. This is a key foundational paper, proving the well-definedness of barcodes using the classification theorem for graded modules over a principal ideal domain. Zomorodian was one of the creators of persistent homology.

Categorical perspectives

Stability theorems  There's a nice summary of stability theorems on page 2 of the paper by Bubenik and Scott listed above.

This page was last changed on 11 March 2019. Home.