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.

Intro
Generalized Persistence Modules
Persistent Homology
Workflow Diagram/Algebraic Stability
Bottleneck Metric Example
Interleaving Metrics
Metric on P
Isometry Theorem 1
Variety of Interleavings
Isometry Theorem 2
Stability Theorem 3
Thank You