BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hannah Santa Cruz (Vrije University Amsterdam - Netherlands) DTSTART:20241101T160000Z DTEND:20241101T170000Z DTSTAMP:20260423T041526Z UID:GEOTOP-A/88 DESCRIPTION:Title: Hodge Laplacians on Sequences\nby Hannah Santa Cruz (Vrije Universit y Amsterdam - Netherlands) as part of GEOTOP-A seminar\n\n\nAbstract\nHodg e Laplacians have been previously proposed as a natural tool for understan ding higher-order interactions in networks and directed graphs. In this ta lk\, we will cover a Hodge-theoretic approach to spectral theory and dimen sionality reduction for probability distributions on sequences and simplic ial complexes. We will introduce a feature space based on the Laplacian e igenvectors associated to a set of sequences\, and will see these eigenve ctors capture the underlying geometry of our data. Furthermore\, we will s how this Hodge theory has desirable properties with respect to natural nul l-models\, where the underlying vertices are independent. Specifically\, w e will see the appropriate Hodge Laplacian has an integer spectrum with hi gh multiplicities\, and describe its eigenspaces. Finally\, we will cover a simple proof showing the underlying cell complex of sequences has trivia l reduced homology.\n LOCATION:https://researchseminars.org/talk/GEOTOP-A/88/ END:VEVENT END:VCALENDAR