Schedule
The seminar is now over. Thanks to everyone for their participation.
We met on Mondays, 4.105.00pm, 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: HenryLouis de Kergolay, Stability

Monday 18 February: no seminar (Carnival of Creative Learning)

Monday 25 February: HenryLouis de Kergolay, More on stability

Monday 4 March: Double bill: (1) HenryLouis 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.
Twopage 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 welldefinedness 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.
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