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SUMMARY:Jacob Leygonie (University of Oxford - UK)
DTSTART:20211203T160000Z
DTEND:20211203T170000Z
DTSTAMP:20260423T022928Z
UID:GEOTOP-A/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GEOTOP-A/9/"
 >Inverse Problems for Persistent Homology</a>\nby Jacob Leygonie (Universi
 ty of Oxford - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nPersistent H
 omology (PH) is a widely used topological descriptor for data. In order to
  get a systematic understanding of the data science scenarios where PH is 
 successful\, it is crucial to know about its discriminative power\, i.e. t
 he ability to identify and disambiguate patterns in the data\, or in other
  words it is crucial to know about the information loss and the invariance
 s of PH. Formally these interrogations translate into the following invers
 e problem: Given an element in the image of PH\, a so-called barcode D\, w
 hat is the fiber (pre-image) of PH over D? There are several ways of defin
 ing PH: for point clouds in a metric space\, for filter functions on a sim
 plicial complex and for continuous functions on an arbitrary space\, to na
 me a few. Hence there are as many inverse problems to address. In this tal
 k I will review the simplicial situation as well as that of Morse function
 s on a smooth manifold\, with the aim of showing some geometrically surpri
 sing fibers and transmitting my interest for these intricate inverse probl
 ems.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/9/
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