BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Fernando Galaz-García (Durham University - UK) DTSTART:20230602T160000Z DTEND:20230602T170000Z DTSTAMP:20260423T041509Z UID:GEOTOP-A/44 DESCRIPTION:Title: Metric geometry of spaces of persistence diagrams\nby Fernando Galaz -García (Durham University - UK) as part of GEOTOP-A seminar\n\n\nAbstrac t\nPersistence diagrams are central objects in topological data analysis. They are pictorial representations of persistence homology modules and des cribe topological features of a data set at different scales. In this talk \, I will discuss the geometry of spaces of persistence diagrams and conne ctions with the theory of Alexandrov spaces\, which are metric generalizat ions of complete Riemannian manifolds with sectional curvature bounded bel ow. In particular\, I will discuss how one can assign to a metric pair $(X \,A)$ a one-parameter family of pointed metric spaces of (generalized) per sistence diagrams $D_p(X\,A)$ with points in $(X\,A)$ via a family of func tors $D_p$ with $p\\in [1\,\\infty]$. These spaces are equipped with the p -Wasserstein distance when $p\\geq 1$ and the bottleneck distance when $p= \\infty$. The functors $D_p$ preserve natural metric properties of the spa ce $X$\, including non-negative curvature in the triangle comparison sense when $p=2$. When $p=\\infty$\, the functor $D_\\infty$ is sequentially co ntinuous with respect to a suitable notion of Gromov–Hausdorff convergen ce of metric pairs. When $(X\,A) = (\\mathbb{R}^2\,\\Delta)$\, where $\\De lta$ is the diagonal of $\\mathbb{R}^2$\, one recovers previously known pr operties of the usual spaces of persistence diagrams. This is joint work w ith Mauricio Che\, Luis Guijarro\, Ingrid Membrillo Solis\, and Motiejus V aliunas.\n\nhttps://arxiv.org/abs/2109.14697\n\nhttps://arxiv.org/abs/2205 .09718\n LOCATION:https://researchseminars.org/talk/GEOTOP-A/44/ END:VEVENT END:VCALENDAR