BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ran Levi (University of Aberdeen - UK) DTSTART:20230901T160000Z DTEND:20230901T170000Z DTSTAMP:20260423T022840Z UID:GEOTOP-A/49 DESCRIPTION:Title: Differential Calculus for Modules over Posets\nby Ran Levi (Universi ty of Aberdeen - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nThe concep t of a persistence module was introduced in the context of topological dat a analysis. In its original incarnation a persistence module is defined to be a functor from the poset of nonnegative real numbers with theory natur al order to the category of vector spaces and homomorphisms. These are ref erred to as single parameter persistence modules and are a fundamental and useful concept in topological data analysis when the source data depends on a single parameter. The concept naturally lends itself to generalisatio n\, and one may consider persistence modules as functors from an arbitrary poset (or more generally an arbitrary small category) to some abelian tar get category. In other words\, a persistence module is simply a representa tion of the source category in the target abelian category. As such much r esearch was dedicated to studying persistence modules in this context. Uns urprisingly\, it turns out that when the source category is more general t han a linear order\, then its representation type is generally wild. In pa rticular\, keeping in mind that persistence module theory is supposed to b e applicable\, computability of general persistence modules is very limite d. In this talk I will describe the background and motivation for persiste nce module theory and introduce a new set of ideas for local analysis of p ersistence module by methods borrowed from spectral graph theory and multi variable calculus.\n LOCATION:https://researchseminars.org/talk/GEOTOP-A/49/ END:VEVENT END:VCALENDAR