Codes and Expansions (CodEx) Seminar

Henry Adams (Colorado State University)
The topology of projective codes

The goal of this talk is to explain the relationships between four objects:

  1. Packings and coverings in projective space,
  2. The Borsuk-Ulam theorem (a classic result in topology),
  3. Vietoris-Rips complexes (used in topological data analysis), and
  4. Gromov-Hausdorff distances (used in shape matching applications).
The CodEx audience has more experience than I do on topic (1), and I will ask for references you recommend on packings and coverings in projective space. I will assume no familiarity with topics (2)-(4), which I will introduce. For an arXiv preprint on some of these topics, see arXiv:2106.14677.