Exemplars of Sheaf Theory in TDA

Explore four case studies of sheaves and cosheaves in topological data analysis in this 57-minute conference talk. Delve into examples of (co)sheaves in the small, including level set persistence and decorated merge trees. Examine (co)sheaves in the large, focusing on understanding the space of merge trees as a stratified map to the space of barcodes and the development of a new "sheaf of sheaves" that organizes the persistent homology transform over different shapes. Gain insights into the application of sheaf theory in TDA through these exemplars presented by Justin Curry for the Applied Algebraic Topology Network.