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This talk explores the relationship between matchings and persistence barcodes in one-parameter persistence. Discover how Andrea Guidolin presents a new type of matchings associated with morphisms of persistence modules, contrasting them with the induced matchings developed by Bauer and Lesnick. Learn about the interaction between these different types of matchings and a cost notion for morphisms based on p-norms of persistence modules. The presentation concludes with a discussion on the implications of these findings for the algebraic stability of persistence barcodes. This 47-minute lecture from the Applied Algebraic Topology Network is based on joint research with Jens Agerberg, Isaac Ren, and Martina Scolamiero.
