BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bei Wang (University of Utah - USA) DTSTART:20210820T150000Z DTEND:20210820T160000Z DTSTAMP:20260423T022923Z UID:GEOTOP-A/1 DESCRIPTION:Title: Sheaf-Theoretic Stratification Learning From Geometric and Topological Pe rspectives\nby Bei Wang (University of Utah - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nWe investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms fram ed in terms of a sheaf on a partially ordered set with the Alexandroff top ology. We prove that the resulting decomposition is the unique minimal str atification for which the strata are homogeneous and the given sheaf is co nstructible. In particular\, when we choose to work with the local homolog y sheaf\, our algorithm gives an alternative to the local homology transfe r algorithm given in Bendich et al. (2012)\, and the cohomology stratifica tion algorithm given in Nanda (2020). Additionally\, we give examples of s tratifications based on the geometric techniques of Breiding et al. (2018) \, illustrating how the sheaf-theoretic approach can be used to study stra tifications from both topological and geometric perspectives. This approac h also points toward future applications of sheaf theory in the study of t opological data analysis by illustrating the utility of the language of sh eaf theory generalizing existing algorithms. This is joint work with Adam Brown.\n LOCATION:https://researchseminars.org/talk/GEOTOP-A/1/ END:VEVENT END:VCALENDAR