Title: Sheaves as a Foundation for Persistence
Speaker: Justin Curry (Duke University)
Abstract: Circa 2010, Carlsson, de Silva, and Morozov initiated the study of zig-zag persistence for topological data analysis. In this introductory talk, I will describe how zig-zag persistence, level-set persistence, and parametrized homolog (ala Kalisnik) can be phrased in terms of pre-sheaves or pre-cosheaves, depending on whether one uses cohomology or homology. I will point out some problems with this approach and why working with the associated sheaves and cosheaves should be preferred. I will also describe how a folk theorem of MacPherson, proved in my thesis, can provide more structure when working with multi-dimensional persistence.
Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html