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SUMMARY:Generalizations of the Rips filtration for quasi-metric spaces wit
 h corresponding stability results
DTSTART:20170227T141500
DTEND:20170227T153000
DTSTAMP:20260919T212642Z
UID:44629c18ac89991807a20c4e0c6176c02053bef0d9f75d1dc174ddd8
CATEGORIES:Conferences - Seminars
DESCRIPTION:Kate Turner (EPFL)\nRips filtrations over a finite metric spac
 e and their corresponding persistent homology are prominent methods in Top
 ological Data Analysis to summarize the ``shape'' of data. For finite metr
 ic space X and distance r the traditional Rips complex with parameter r is
  the flag complex whose vertices are the points in X and whose edges are {
 [x\,y]: d(x\,y)≤ r}. From considering how the homology of these complexe
 s evolves we can create persistence modules (and their associated barcodes
  and persistence diagrams). Crucial to their use is the stability result t
 hat says if X and Y are finite metric space\, then the bottleneck distance
  between persistence modules constructed by the Rips filtration is bounded
  by 2d_{GH}(X\,Y) (where d_{GH} is the Gromov-Hausdorff distance). Using t
 he asymmetry of the distance function we define four different constructio
 ns analogous to the persistent homology of the Rips filtration and show th
 ey also are stable with respect to the Gromov-Hausdorff distance. These di
 fferent constructions involve ordered-tuple homology\, symmetric functions
  of the distance function\, strongly connected components\, and poset topo
 logy.
LOCATION:GC A1 416 https://plan.epfl.ch/theme/generalite_thm_v2?lang=en&ro
 om=gc%20a1%20416&dim_floor=1&dim_lang=en&tree_group_layers_centres_nevralg
 iques=information_epfl%2Cguichet_etudiants&tree_group_layers_acces=metr
STATUS:CONFIRMED
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