BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bjørnar Gullikstad Hem (EPFL) DTSTART:20251222T123000Z DTEND:20251222T133000Z DTSTAMP:20260422T140031Z UID:BilTop/131 DESCRIPTION:Title: Decomposing multipersistence modules using functor calculus\nby Bjør nar Gullikstad Hem (EPFL) as part of Bilkent Topology Seminar\n\nLecture h eld in SA 141.\n\nAbstract\nMultiparameter persistent homology has attract ed growing interest in the topological data analysis community\, in part d ue to its ability to handle noisy data. However\, unlike the single-parame ter case\, multipersistence modules do not generally admit an interval dec omposition\, which makes the multiparameter setting considerably more comp licated. Nevertheless\, there exist certain sufficient conditions that gua rantee interval decomposability\, such as a locally defined condition call ed middle exactness.\nIn this talk\, I introduce poset cocalculus\, which is a variant of functor (co)calculus that is defined for functors from a p oset to a model category. The motivation for this framework lies in the re levance of functors from posets to the model category of chain complexes o ver a field\, as any multipersistence module is the homology of such a fun ctor. Poset cocalculus provides tools for relating local conditions on the se functors to their global structure. I apply this to give a novel\, more synthetic proof of the fact that middle exactness implies interval decomp osability.\n LOCATION:https://researchseminars.org/talk/BilTop/131/ END:VEVENT END:VCALENDAR