Persistence Diagram Bundles- A Multidimensional Generalization of Vineyards

Explore the multidimensional generalization of vineyards in topological data analysis through a comprehensive lecture on Persistence Diagram Bundles. Delve into the challenges of analyzing evolving data sets with multiple parameters and discover how Persistence Diagram (PD) bundles overcome the limitations of traditional vineyards and multiparameter persistent homology. Learn about the concept, efficient computation algorithms, and unique properties of PD bundles, including their ability to exhibit monodromy. Gain insights into the potential applications of this innovative approach in analyzing complex, time-evolving point clouds with additional system parameters.

Intro
Persistent Homology (PH)
Existing approach: Vineyards
Motivation for new approach: Persistence diagram
Persistence Diagram Bundles
Special cases of PD bundles
Relationship to the fibered barcode in multiparamet
Decomposing a PD bundle into simpler parts
Stratifying the base space
Sections of PD bundles
How can we compute PD bundles?
Review: Computing vineyards
Algorithm for computing PD bundles
Future Applications