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SUMMARY:Harder-Narasimhan Filtrations of Persistence Modules - Marc Ferszt
 and (University of Oxford)
DTSTART:20240117T111000Z
DTEND:20240117T115500Z
UID:TALK210610@talks.cam.ac.uk
DESCRIPTION:The Harder-Narasimhan type of a quiver representation is a fam
 ily of discrete invariants parameterised by a real-valued function (called
  a central charge) defined on the vertices of the quiver. In this talk\, w
 e investigate the strength and limitations of Harder-Narasimhan types for 
 several families of quiver representations which arise in Topological Data
  Analysis. We introduce the skyscraper invariant\, which amalgamates the H
 N types along central charges supported at single vertices\, and show that
  it is strictly finer than the rank invariant. We also study\, for several
  families of persistence modules\, the set of central charges for which th
 e HN type is a complete invariant.\nThis work is detailed in the preprint 
 https://arxiv.org/abs/2303.16075. It is a joint work with Emile Jacquard\,
  Vidit Nanda and Ulrike Tillmann.
LOCATION:Seminar Room 2\, Newton Institute
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