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SUMMARY:Emerson Escolar (Kobe University)
DTSTART:20250422T060000Z
DTEND:20250422T070000Z
DTSTAMP:20260423T021229Z
UID:OISTRTS/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OISTRTS/67/"
 >Representation Theory and (Barcoding) Invariants for Persistence</a>\nby 
 Emerson Escolar (Kobe University) as part of OIST representation theory se
 minar\n\n\nAbstract\nPersistent homology is one of the main tools of topol
 ogical data analysis\, which has seen rapid growth recently. In the first 
 part of this talk\, I discuss some of the ways representation theory is be
 ing used for persistent homology\, focusing on "invariants". In particular
 \, the persistence barcode\, which can be obtained from an indecomposable 
 decomposition of a persistence module into intervals\, plays a central rol
 e. For multi-parameter persistent homology\, where persistence modules are
  no longer always interval-decomposable\, many alternative invariants have
  been proposed. Naturally\, identifying the relationships among invariants
 \, or ordering them by their discriminating power\, is a fundamental quest
 ion. The second part of this talk\, based on arXiv:2412.04995\, addresses 
 this. I discuss our formalization of the notion of "barcoding invariants"\
 , which generalizes the persistence barcode\, and results concerning the c
 omparison of their discriminating powers.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/67/
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