L-P Metrics on Multiparameter Persistence Modules
Explore a comprehensive lecture on l_p-metrics for multiparameter persistence modules in topological data analysis. Delve into the generalization of p-Wasserstein distance on barcodes to multi-parameter persistence modules, introducing two key generalizations: d_I^p and d_M^p. Examine how these distances relate to the interleaving and matching distances, and discover their valuable properties. Investigate the continuity of 2-parameter multicover persistent homology, uncovering nuances in the stability theory not captured by the interleaving distance alone. Learn about the collaborative work with Havard Bjerkevik and gain insights from this talk, which was part of the "Topological Data Analysis - Theory and Applications" workshop supported by the Tutte Institute and Western University.