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SUMMARY:Baris Coskunuzer
DTSTART:20231211T103000Z
DTEND:20231211T113000Z
DTSTAMP:20260422T135903Z
UID:BilTop/72
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BilTop/72/">
 Filling Radius and Persistent Homology</a>\nby Baris Coskunuzer as part of
  Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbstract\nIn this 
 talk\, we discuss interesting relations between notions from applied topol
 ogy and metric geometry in point cloud setting. First\, we introduce sever
 al notions in both fields to measure the size of a manifold. Then\, for a 
 point cloud X in R^n\, we relate the life spans of the topological feature
 s to their extrinsic and Gromov’s filling radius in R^n\, and by using t
 his relation\, we give bounds for them with Urysohn width. Next\, we discu
 ss an interesting relationship between the life spans of the topological f
 eatures in PD_k(X) in R^n and l^\\infty principal components (PCA_\\infty)
  of the point cloud X.\n
LOCATION:https://researchseminars.org/talk/BilTop/72/
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