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Topology, Geometry and Data Seminar - Nick Bermingham

bermingham
September 17, 2024
4:00 pm - 5:00 pm
Cockins 312

Nick Bermingham
The Ohio State University

Title
The Persistent Cup Length Function

Abstract
In Topological Data Analysis we are often trying to find easily computable topological invariants for a given dataset for the purposes of comparison with other datasets or individual analysis of the features of a given dataset. One such invariant is the persistent cup length function which utilises the ring structure of the cohomology groups at each point in the filtration to enrich the standard persistent cohomology barcodes. This function can be computed by creating a persistent cup length diagram from the collection of cocycle representatives used to calculate the persistent cohomology barcodes in programs like Ripser.

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Seminar - Topology, Geometry and Data