BEGIN:VCALENDAR
VERSION:2.0
PRODID:www.dresden-science-calendar.de
METHOD:PUBLISH
CALSCALE:GREGORIAN
X-MICROSOFT-CALSCALE:GREGORIAN
X-WR-TIMEZONE:Europe/Berlin
BEGIN:VTIMEZONE
TZID:Europe/Berlin
X-LIC-LOCATION:Europe/Berlin
BEGIN:DAYLIGHT
TZNAME:CEST
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
DTSTART:19810329T030000
RRULE:FREQ=YEARLY;INTERVAL=1;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZNAME:CET
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
DTSTART:19961027T030000
RRULE:FREQ=YEARLY;INTERVAL=1;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
UID:DSC-22129
DTSTART;TZID=Europe/Berlin:20250804T130000
SEQUENCE:1754285820
TRANSP:OPAQUE
DTEND;TZID=Europe/Berlin:20250804T140000
URL:https://www.dresden-science-calendar.de/calendar/de/detail/22129
LOCATION:MPI-CBG\, Pfotenhauerstraße 10801307 Dresden
SUMMARY:Sandt: Persistence Modules of Metric Space Approximations: Stabilit
 y under Perturbations
CLASS:PUBLIC
DESCRIPTION:Speaker: Philip Sandt\nInstitute of Speaker: ETH Zürich\nTopic
 s:\n\n Location:\n  Name: MPI-CBG (MPI-CBG CSBD SR Ground Floor (VC))\n  S
 treet: Pfotenhauerstraße 108\n  City: 01307 Dresden\n  Phone: +49 351 210
 -0\n  Fax: +49 351 210-2000\nDescription: We suppose that we are given a p
 oint cloud\, which we think of as a finite sample of points from some geom
 etric object. This situation can arise in data analysis\, where high-dimen
 sional data has to be analyzed\, but it could also be a sample from a subm
 anifold of Rn. The mathematical formalism that studies such point clouds i
 s called persistence. It works by assigning a persistence module to a poin
 t cloud. A persistence module is a purely algebraic object but is able to 
 capture a lot of topological information about the data set. We can look a
 t the data set from the point of view of di!erent scales\, and for each sc
 ale the persistence module gives us feedback on the number of connected co
 mponents\, the number of holes and their higher dimensional analogues at e
 ach scale. At di!erent scales\, di!erent geometric shapes become apparent 
 in the data set. The question which we investigate is the following. How d
 oes the persistence module associated to a point cloud change when the poi
 nt cloud is replaced by a perturbed version of itself\, for example if we 
 sample with noise? Investigating such a question will require introducing 
 distance functions on the level of both the persistence modules and the pe
 rturbation between sets. The main result is that the amount by which the p
 ersistence modules di!er is bounded by the amount of perturbation between 
 the data sets. This is called the stability inequality.
DTSTAMP:20260611T205937Z
CREATED:20250729T053806Z
LAST-MODIFIED:20250804T053700Z
END:VEVENT
END:VCALENDAR