**Time and location:**Thursdays, 2:00-3:30, starting May 3; MC107**Organizer:**Dan Christensen**E-mail:**`jdc@uwo.ca`

- April 11 and 13, Dan Christensen, Topological data analysis: persistent homology. Mostly chalk, with a few Slides.
- May 3, Alex Rolle, The HDBSCAN* clustering algorithm. Slides.
- May 10, Jianing Huang, Computation of persistent homology. Slides.
- May 17, James Richardson, Kleinberg's impossibility theorem for clustering.
- May 24, Brandon Doherty, The Cech complex. Slides.
- May 31, Koundinya Vajjha, Topological Data Analysis of financial time series. Slides, TDA tutorial in R, TDA finance example in R.
- June 7, Andrew Herring, The Mapper algorithm. Slides.
- June 14, Tim Pollock, Clusters and functors. Slides.
- June 21, Luis Scoccola, Topological Data Analysis in R. Files.
- June 28, Jianing Huang, A brief introduction to multi-dimensional persistence. Slides.

- Ghrist, Barcodes: the persistent topology of data
- Ghrist, Homological algebra and data
- Carlsson, Topology and data
- Carlsson, Topological pattern recognition for point cloud data
- Edelsbrunner and Harer, Persistent homology — a survey
- Chazal and Michel, An introduction to TDA: fundamental and practical aspects for data scientists
- And lots more!

- The Cech complex, how it compares to the Vietoris-Rips complex. (Brandon.)
- Carlsson-Mémoli, characterization of Vietoris-Rips as a clustering algorithm. (Tim.)
- Density sampling.
- Clustering. (Covered by Alex, but maybe there's more to say?)
- More details about case studies, such as those mentioned in Dan's second talk.

For the brave: find a data set and run TDA on it to see what you find! (Luis.) - The Mapper algorithm, which is used by many of the interesting applications. (Andrew.)
- Sublevel set filtration, based on a real-valued function on the data.
- Zig-zag persistence.
- Multi-dimensional persistence. (Jianing.)
- More about how the computations are done, e.g. Mayer-Vietoris spectral sequence. (Mostly covered by Jianing.)
- More about barcodes: the stronger classification theorems, metrics on the space of barcodes, etc.
- Manifold estimation, dimension estimation.
- Creating smaller complexes for efficiency: Landmark points, Delaunay complex, alpha-complex, witness complex, etc.
- Feel free to suggest other topics! Skim some of the references above for ideas.

Summer School on Topological Data Analysis for Banking and Finance, July 16-27, 2018, UWO.