Workshop on Topology: Identifying Order in Complex Systems

Parameters in indexed homology

Motivated by thematic similarities between persistent homology and magnitude homology, we describe a simplicial construction associated to a metric space. This construction is determined by (apart from the metric space itself) a choice of two parameters, which we may take to be real-valued. Applying homology pointwise, we get persistent homology on one end of the possible choices of parameters, and magnitude homology on the opposite end. Time permitting, we describe some modest applications of this perspective.

Date & Time

October 09, 2020 | 2:00pm – 3:30pm

Location

Remote Access - see Zoom link below

Speakers

Simon Cho

Affiliation

University of Michigan

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