BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Magnus Botnan (VU Amsterdam - Netherlands) DTSTART:20250411T160000Z DTEND:20250411T170000Z DTSTAMP:20260423T022915Z UID:GEOTOP-A/99 DESCRIPTION:Title: At the extremal points of filtered spaces\nby Magnus Botnan (VU Amst erdam - Netherlands) as part of GEOTOP-A seminar\n\n\nAbstract\nIn this ta lk\, I will present two recent projects exploring extremal properties of f lag complexes and structural aspects of multiparameter persistence.\n\nIn the first part (joint with Lies Beers\, accepted to SoCG '25)\, we investi gate fundamental yet surprisingly challenging questions about the Vietoris –Rips barcode in degree k homology. Given a data set of N points\, what is the maximum number of bars in its barcode? What is the maximal total pe rsistence? How long can the longest bar be? We establish tight bounds in m any cases but also uncover intriguing open problems. I will place our resu lts in the context of earlier work by Kozlov and others\, highlighting key challenges that remain.\n\nThe second part (joint with U. Bauer\, S. Oppe rmann\, and J. Steen) focuses on multiparameter persistence in homology de gree 0. It is well known that any diagram of vector spaces (over a prime f ield) and linear maps can be realized via degree k homology applied to a d iagram of simplicial complexes. But what if we restrict to degree 0? This is equivalent to studying diagrams of vector spaces and linear maps arisin g from diagrams of sets and set maps—an inherently more difficult settin g. While our recent work develops a general theory\, I will focus on the s pecific case of grids which is closely related to clustering.\n LOCATION:https://researchseminars.org/talk/GEOTOP-A/99/ END:VEVENT END:VCALENDAR