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SUMMARY:Mario Gómez Flores (The Ohio State University)
DTSTART:20211109T210000Z
DTEND:20211109T220000Z
DTSTAMP:20260423T004132Z
UID:TDGA/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TDGA/4/">Cur
 vature Sets Over Persistence Diagrams</a>\nby Mario Gómez Flores (The Ohi
 o State University) as part of Topology\, Geometry\, & Data Analysis (TGDA
 ) Seminar\n\n\nAbstract\nWe study an invariant of compact metric spaces in
 spired by the Curvature Sets defined by Gromov. The (n\,k)-Persistence Set
  of X is the collection of k-dimensional VR persistence diagrams of any su
 bset of X with n or less points. This research seeks to provide a cheaper 
 persistence-like invariant for metric spaces\, as the computation of the V
 R complex becomes prohibitive once the input reaches a certain size. I'll 
 focus on the case n=2k+2\, where we can find a geometric formula to calcul
 ate the VR persistence diagram of a space with n points. We explore the ap
 plication of this formula to the characterization of persistence sets of s
 everal spaces\, including circles\, higher dimensional spheres\, and surfa
 ces with constant curvature. We also show that persistence sets can detect
  the homotopy type of a certain family of graphs.\n
LOCATION:https://researchseminars.org/talk/TDGA/4/
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