Open Collections

Towards an Analytic Understanding of the Persistence Map

Banff International Research Station for Mathematical Innovation and Discovery

If TDA wants to move away from the study of persistence diagrams a posteriori and towards the construction of analytical models or predictions of persistence diagrams from calculus-based physics-type models, an analytical (rather than algorithmic) study of the persistence map must be undertaken. Beyond stability, remarkably few things are known about the persistence map. In this talk, I will provide a complete characterization of the image and the fiber of the persistence map for time series (functions from the interval to the real line) as detailed in a recent arXiv preprint (arxiv.org/abs/1706.06059). This talk will require very little background knowledge and will contain several open problems.

Mathematics; Algebraic topology; Probability theory and stochastic processes; Data mining

video/mp4

Author affiliation: Duke University

2018-01-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64474

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/