CS 7870, Seminar in theoretical computer science — Topological methods for the analysis of data

Syllabus: pdf

Lectures:

  • Lecture 1 [01/06/2025] pdf: Intro to Topological Data Analysis

  • Lecture 2 [01/09/2025] pdf: Metric spaces and generalizations (extended, pseudo and distance)

  • Lecture 3 [01/13/2025] pdf: Metric topology: Open sets, closed sets and continuous functions

  • Lecture 4 [01/16/2025] pdf: Topological spaces, continuity, homeomorphisms, homotopies

  • Lecture 5 [01/23/2025] pdf: Homotopy equivalence, topological inference compactness

  • Lecture 6 [01/27/2025] pdf: The medial axis, the reach and homotopy inference of manifolds

  • Lecture 7 [01/30/2025] pdf: Simplicial complexes, the Rips, Nerve and Cech complexes

  • Lecture 8 [02/03/2025] pdf: Computing Rips and Cech complexes, Geometric realization, The nerve lemma