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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Harder-Narasimhan Filtrations of Persistence Modul
 es - Marc Fersztand (University of Oxford)
DTSTART;TZID=Europe/London:20240117T111000
DTEND;TZID=Europe/London:20240117T115500
UID:TALK210610AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/210610
DESCRIPTION:The Harder-Narasimhan type of a quiver representat
 ion is a family of discrete invariants parameteris
 ed by a real-valued function (called a central cha
 rge) defined on the vertices of the quiver. In thi
 s talk\, we investigate the strength and limitatio
 ns of Harder-Narasimhan types for several families
  of quiver representations which arise in Topologi
 cal Data Analysis. We introduce the skyscraper inv
 ariant\, which amalgamates the HN types along cent
 ral charges supported at single vertices\, and sho
 w that it is strictly finer than the rank invarian
 t. We also study\, for several families of persist
 ence modules\, the set of central charges for whic
 h the 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
CONTACT:
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