Title: Open Problems and Higher Categories in Persistence
Speaker: Justin Curry (Duke University)
Abstract: Recent work by MacPherson and Patel advances a new foundation for persistence using 2-categories. I will describe in elementary terms this theory, and a simpler version in 1-dimension that uses elementary constructions of limits and colimits. The image of the map from the limit to the colimit provides a different version of "persistence" for sheaves and other functors, that I believe is useful. Time permitting, I will show how higher categories appear in discrete Morse theory for sheaves and elementary problems in two-dimensional persistence.
Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html