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
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
the persistent topology of data.
The plan is to use this as our main reference and our guide.
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.
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
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.)
Computational and applied
topology, tutorial. Chapter 7 is about persistent homology.
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,
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
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.