David Meyer - Some Algebraic Stability Theorems for Generalized Persistence Modules

Explore a 53-minute lecture on algebraic stability theorems for generalized persistence modules presented by David Meyer. Delve into the algebraic interpretation of generalized persistence modules as finitely-generated modules for poset algebras. Learn about the isometry theorem of Bauer and Lesnick and its algebraic analogue for a wide range of posets. Discover how the interleaving metric of Bubenik, de Silva, and Scott can be realized as a bottleneck metric incorporating algebraic information. Examine the concept of comparing generalized persistence modules from data using a directed set of algebras and recovering classical interleaving distance through limits. Investigate minimal conditions for stability in general persistence modules for quivers, utilizing a bottleneck metric derived from a weighted graph metric on the Auslander-Retien quiver of the module category. Follow the lecture's structure, covering topics such as persistent homology, workflow diagrams, algebraic stability, bottleneck metric examples, interleaving metrics, and various stability theorems.