Christian Hirsch EVA Talk Preview
From Anna Munro
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Name: Christian Hirsch
Talk Title: Extremal lifetimes of persistent loops and holes
Abstract: Persistent homology captures the appearances and disappearances of topological features such as loops and holes when growing disks centered at a Poisson point process. We study extreme values for the lifetimes of features dying in bounded components and with birth resp. death time bounded away from the threshold for continuum percolation. First, we describe the scaling of the minimal lifetimes for general feature dimensions, and of the maximal lifetimes for holes in the Čech complex. Then, we proceed to a more refined analysis and establish Poisson approximation for large lifetimes of holes and for small lifetimes of loops. Finally, we also study the scaling of minimal lifetimes in the Vietoris-Rips setting and point to a surprising difference to the Čech complex. This talk is based on joint work with N. Chenavier.
This talk is an invited talk at EVA 2021. View the programme here.