Parametrized persistent homology

07/02/2020, 14:00 - 15:00 in MAP/0G/014

Giansiracusa, Jeffrey (Swansea University)


Abstract:

Persistent homology takes a family of simplicial complex depending on a single real parameter and describes how the homology varies in the family in terms of a barcode. When the family depends on two or more parameters then there is no way of giving a complete combinatorial description of the homology; this is the challenge of multiparameter persistent homology. Nevertheless, incomplete combinatorial descriptions can be very useful in practice. I will describe how the stability properties of 1-parameter persistent homology can be used to ‘integrate’ 1-parameter barcodes along a second parameter direction to obtain a 2-dimension analogue of barcodes.

Mathematical Sciences Research Centre