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SUMMARY:Eric Goubault (Ecole Polytechnique - France)
DTSTART:20240531T160000Z
DTEND:20240531T170000Z
DTSTAMP:20260423T041527Z
UID:GEOTOP-A/70
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GEOTOP-A/70/
 ">Directed homology and persistence modules</a>\nby Eric Goubault (Ecole P
 olytechnique - France) as part of GEOTOP-A seminar\n\n\nAbstract\nIn this 
 talk\, I will give a self-contained account of a construction for a direct
 ed homology theory based on modules over algebras\, linking it to both per
 sistence homology and natural homology.\n\nPersistence modules have been i
 ntroduced originally for topological data analysis\, where the data set se
 en at different « resolutions » is organized as a filtration of spaces. 
 This has been further generalized to multidimensional persistence and « g
 eneralized » persistence\, where a persistence module was defined to be a
 ny functor from a partially ordered set\, or more generally a preordered s
 et\, to an arbitrary category (in general\, a category of vector spaces).\
 n\nThis talk will be concerned with a more « classical » construction of
  directed homology\, mostly for precubical sets here\, based on (bi)module
 s over (path) algebras\, making it closer to classical homology with value
  in modules over rings\, and of the techniques introduced for persistence 
 modules. Still\, this construction retains the essential information that 
 natural homology is unveiling. Of particular interest will be the role of 
 restriction and extension of scalars functors\, that will be central to th
 e discussion of Kunneth formulas\, Mayer-Vietoris and relative homology se
 quences. If time permits as well\, we will discuss some « tameness » iss
 ues\, for dealing with practical calculations.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/70/
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