We explore the perspective of viewing persistence diagrams, or persistence barcodes, as diagrams in the categorical sense. Specifically, we consider functors indexed over the reals and taking values in the category of matchings, which has sets as objects and partial bijections as morphisms.\ This yields a categorical structure on barcodes, turning the bottleneck distance into an interleaving distance, and allowing for a simple reformulation of the induced matching theorem, which has been used to prove the algebraic stability of persistence barcodes. We will also discuss an explicit construction of a barcode for a pointwise finite-dimensional persistence module that doesn’t require a decomposition into indecomposable interval summands, and that is actually functorial on monomorphisms of persistence modules (along with a dual construction, which is functorial on epimorphisms). This is joint work with Michael Lesnick (Albany).
Mittwoch, den 12. Juni 2019 um 11.00 Uhr, in Mathematikon, INF 205, Konferenzraum, 5. Stock Mittwoch, den 12. Juni 2019 at 11.00, in Mathematikon, INF 205, Konferenzraum, 5. Stock
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Peter Albers