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

- May 3, Alex Rolle
- May 10, Jianing Huang
- Volunteers wanted!

- 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 &emdash; 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.
- Density sampling.
- Clustering.
- Case studies.
- The Mapper algorithm, which is used by many of the interesting applications.
- Sublevel set filtration, based on a real-valued function on the data.
- Multi-dimensional persistence.
- More about how the computations are done, e.g. Mayer-Vietoris spectral sequence.
- 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.

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