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This is a video about Higher Interpolation and Extension for Persistence Modules

Higher Interpolation and Extension for Persistence Modules

May 20, 2016
MBI
Presenters: Peter Bubenik
Length: 51 minutes 51 seconds

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Abstract

Persistence modules are the central algebraic object in topological data analysis. This

motivates the study of the geometry of the space of persistence modules. We isolate an elegant

coherence condition that guarantees the interpolation and extension of sets of persistence

modules. This "higher interpolation" is a consequence of the existence of certain universal

constructions. As an application, it allows one to compare Vietoris-Rips and Cech complexes

built within the space of persistence modules. This is joint work with Vin de Silva and Vidit

Nanda.