Session S27 - Categories and Topology

Wednesday, July 21, 16:30 ~ 17:00 UTC-3

Interleavings and Gromov-Hausdorff Distance

Jonathan Scott

Cleveland State University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

One of the central notions to emerge from the study of persistent homology is that of interleaving distance. It has found recent applications in computational geometry, symplectic and contact geometry, sheaf theory, and phylogenetics. Here we present a general study of this topic, considering interleavings of functors to be solutions to a certain extension problem. By placing the problem in the context of (weighted) bicategories, we identify interleaving distance as a type of categorical generalization of Gromov--Hausdorff distance. As an application we recover a definition of shift equivalences of discrete dynamical systems.

Joint work with Vin de Silva (Pomona College) and Peter Bubenik (U Florida).

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