Exemplars of Sheaf Theory in TDA

15 October 2021
15:00
Justin Curry
Abstract

In this talk I will present four case studies of sheaves and cosheaves in topological data analysis. The first two are examples of (co)sheaves in the small:

(1) level set persistence---and its efficacious computation via discrete Morse theory---and,

(2) decorated merge trees and Reeb graphs---enriched topological invariants that have enhanced classification power over traditional TDA methods. The second set of examples are focused on (co)sheaves in the large:

(3) understanding the space of merge trees as a stratified map to the space of barcodes and

(4) the development of a new "sheaf of sheaves" that organizes the persistent homology transform over different shapes.

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  • Applied Topology Seminar