BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hiroshi Takeuchi (Shiga University\, Japan) DTSTART:20210326T050000Z DTEND:20210326T060000Z DTSTAMP:20260423T004637Z UID:APATG/20 DESCRIPTION:Title: T he persistent homology of a sampled map: on failed reconstructions\nby Hiroshi Takeuchi (Shiga University\, Japan) as part of Asia Pacific Semin ar on Applied Topology and Geometry\n\n\nAbstract\nThis talk introduces a filtration analysis of sampled maps based on persistent homology. The aim is to reconstruct the underlying maps. The key idea is to extend the defin ition of homology-induced maps of correspondences using quiver representat ions. Our definition of homology-induced maps is given by the most persist ent direct summands of representations. The direct summands uniquely deter mine a persistent homology for a sampled map. Compared to existing methods using eigenspace functors\, our filtration analysis represents an importa nt advantage that no prior information related to the eigenvalues of the u nderlying map is required. However\, our reconstruction method does not al ways work. In this talk\, we focus on examples of failed reconstructions.\ n\nThis talk is based on the paper DOI:10.1007/s41468-021-00065-3 (in pres s). The preprint is available at arXiv:1810.11774.\n LOCATION:https://researchseminars.org/talk/APATG/20/ END:VEVENT END:VCALENDAR