Geometry Workshop Obergurgl 2021

k-fold filtrations, or filtrations of k-covers is a natural way of obtaining a two-parameter filtration of a point set and thus examples where multi-parameter persistent homology occurs naturally. In this talk, we will explore the construction of the k-fold filtrations, their structure and the computational challenges it raises. We will then take a look at some ongoing work to approximate the construction in order to reduce the computational cost.