Geometric Approaches on Persistent Homology

Explore geometric approaches to interpreting persistence diagrams in this comprehensive lecture on persistent homology. Delve into new quantitative and geometric descriptions of the "size" or "persistence" of homology classes. Examine a case study analyzing the power filtration on unweighted graphs, and discover explicit bounds for the life spans of homology classes in persistence diagrams across all dimensions. Learn about the collaborative research conducted with Henry Adams, gaining insights into advanced concepts in applied algebraic topology. Access accompanying slides for visual aids and further understanding of the presented material.