BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ippei Obayashi (Center for Advanced Intelligence Project (AIP)\, R IKEN) DTSTART:20201120T050000Z DTEND:20201120T060000Z DTSTAMP:20260423T004701Z UID:APATG/13 DESCRIPTION:Title: F ield choice problem in persistent homology\nby Ippei Obayashi (Center for Advanced Intelligence Project (AIP)\, RIKEN) as part of Asia Pacific S eminar on Applied Topology and Geometry\n\n\nAbstract\nMathematically\, pe rsistent homology is formalized on the homology vector spaces of a filtrat ion and linear maps between the vector spaces induced by the inclusion map s. By encoding the scale information in the filtration\, we can capture th e geometric features of data. The structure theorem of persistent homology ensures the existence and uniqueness of the interval decomposition. A per sistence diagram is given by the interval decomposition. The diagram has t he complete information about the algebraic structure of persistent homolo gy.\n\nWhen we fix the field of the homology vector spaces\, the uniquenes s of the decomposition is ensured. However\, the uniqueness is broken when the field is changed. One easy example is a filtration including a Klein bottle. A more interesting example is given by a Möbius ring.\n\nFrom the above examples\, the following questions naturally arise.\n\n What con dition does ensure the independence of the choice of the field?\n\n Is there an efficient algorithm to check the above condition?\n\n How ofte n does a persistence diagram change as the field changes?\n\nThe aim of ou r research is to answer the above questions. The result is published on Ar xiv[1]. This is joint work with M. Yoshiwaki.\n\n[1] Ippei Obayashi and Mi chio Yoshiwaki. Field choice problem in persistent homology. arXiv:1911.11 350\, 2019.\n LOCATION:https://researchseminars.org/talk/APATG/13/ END:VEVENT END:VCALENDAR