A crash course on TDA (topological data analysis)

In this course, we will review some intuitions and basics of topological data analysis. More precisely, we will learn

1. why and how topology (and geometry) are useful for data analysis;

2. basics of simplicial complexes and simplicial homology;

3. introduction to some geometric simplicial complexes (e.g., Čech complex, Vietoris–Rips complex, ...);

4. basics of persistent homology (PH) and some algorithms for computing PH;

5. some recent research results on persistent homology. In particular, the connection between PH and geometric quantities such as filling radius and systole.