Videos

An alternative way to define persistence on 1D filtrations and how to compute it

Presenter
May 18, 2026
Abstract
In this talk, I will present recent work on defining a different type of barcode, termed as harmonic chain barcode, for a 1D filtration by taking the groups of harmonic chains (cycles that are also cocycles) for the complexes in the filtration. We find that simplex insertions in a 1D filtration produce maps between consecutive harmonic chain groups whose directions can be flipped, yielding a zigzag module. I will also talk about the (cubic-time) algorithm we have for computing the harmonic chain barcode, which turns out to be quite different from the original persistence algorithm. Joint work with Salman Parsa and Bei Wang.