Comparative Stability of Two Zigzag Bottleneck Distances
Explore a 29-minute conference talk examining the comparative stability of two zigzag bottleneck distances in the field of applied algebraic topology. Delve into the natural extension of 1D persistence known as zigzag persistence, its applications, and its potential as an indirect approach to multidimensional persistence. Analyze the bottleneck distances for zigzag modules generated from various mathematical structures, including kan extensions to planar block modules, Auslander-Reiten quivers, and derived categories. Compare and contrast these distances, highlighting their similarities, stark differences, and irreconcilable aspects. Focus on the specific distance derived from the Auslander-Reiten quiver perspective, understanding its place within the broader context of zigzag persistence theory.