Edit Distance and Persistence Diagrams Over Lattices

Edit Distance and Persistence Diagrams Over Lattices

Explore a comprehensive lecture on the development of a functorial pipeline for persistent homology. Delve into the intricacies of adapting filtered simplicial complexes indexed by finite lattices to produce persistence diagrams through Mobius inversion. Discover how the Reeb graph edit distance is adapted to create a stable pipeline, addressing two major challenges in persistent homology: multiparameter persistent homology and functoriality of persistence diagrams. Learn about the collaborative work between Amit Patel and PhD student Alex McCleary, presented as part of the "Topological Data Analysis - Theory and Applications" workshop supported by the Tutte Institute and Western University.