Presentation description

In topological data analysis, the persistent homology pipeline allows us to understand topological structure of a data set in via a barcode - a summary of persistent "holes" across a filtration of simplicial complexes on our data. Some data warrant investigation across multiple dimensions, requiring the use of filtrations indexed by more than one parameter; describing key info for these multidimensional filtrations requires multiple barcodes. We aim to classify and count such sets of barcodes.