Žiga Virk - Information Encoded in Persistence Diagrams

Explore the rich information encoded in persistence diagrams through this comprehensive 47-minute lecture by Žiga Virk. Delve into various interpretations of persistence diagram components and their relationships to underlying space properties. Examine concepts such as homology, shortest 1-dimensional homology basis in geodesic spaces, locally shortest loops, systole, homotopy height, and contraction subspaces. Investigate proximity properties and critical simplices rigidity. Learn about topological, combinatorial, and geometric footprints, as well as persistence barcodes. Gain insights into practical applications and participate in a Q&A session to deepen your understanding of this complex topic in applied algebraic topology.

Introduction
Topological footprints
Onedimensional homology
Combinatorial footprint
Global conditions
Local conditions
Geometric footprint
Footprint of proximity
Footprint of rigidity
Persistence barcodes
Geometric footprints
Applications
QA