New Results in Computing Zigzag and Multiparameter Persistence

Explore new advancements in computing zigzag and multiparameter persistence in this 53-minute conference talk. Delve into the efficiency gap between zigzag and non-zigzag persistence, discovering how to convert zigzag filtrations to non-zigzag filtrations with minimal cost. Learn about the relationship between generalized rank invariants in 2-parameter persistence and zigzag modules. Examine the improved algorithm for determining interval decomposability in 2-parameter modules. Cover topics including persistent homology, standard persistence, applications of zigzag persistence, non-repetitive to up-down filtrations, and future work in the field.

Intro
Persistent homology
Standard persistence
Application of Zigzag persistence
non-Zigzag Vs. Zigzag persistence
Overview of Fast Zigzag
Non-repetitive to Up-down
Up-down Filtration
Extended to Non-zigzag
Overall Conversions
2 parameter persistence and rank invariant
Future work