A topologist is a person, who doesn't know a donut from a coffee cup
Introduction. Basic definitions and concepts: metrics, continuous maps, homeomorphisms, homotopy type.
Textbook: Chapter 1
Triangulations in the plane, Voronoi diagram, Delaunay triangulation.
Textbook: Chapter 2
Geometric simplicial complexes, Abstract simplicial complexes, Euler characteristic
Textbook: Chapter 3
Carve a pumpkin
Simplicial complexes on data sets:
Interleaving.
Textbook: Chapter 5
Algebraic groups. Intuition and idea of homology.
Textbook: Chapter 6, idea of chapter 7
Computing homology
Textbook: Chapters 7 and 8.1
Persistent homology
Textbook: Chapter 9
Filtrations, persistence modules, interleavings, Gromov-Hausdorff distance
Textbook: Chapters 9 and 10
Stability theorem for persistent homology, Wasserstein distance, further developments of persistence, examples of applications
Textbook: Chapter 10
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