Ephemeral Persistence Modules and Distance Comparison
Explore the intersection of sheaf theory and persistent homology in this 30-minute lecture from the Applied Algebraic Topology Network. Delve into the concept of ephemeral persistence modules and their role in comparing different approaches to studying persistent modules. Examine how sheaf-theoretic methods are applied to filtered and multi-filtered topological spaces, with a focus on the Alexandrov and gamma topologies. Learn about the definition of ephemeral multi-persistent modules and their relationship to gamma-sheaves. Investigate key pseudo-distances in persistence theory, including interleaving and convolution distances, and understand the isometry theorems connecting various categories of persistence modules. Gain insights from joint research with Nicolas Berkouk on this cutting-edge topic in applied algebraic topology.