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SUMMARY:Large-scale geometry of the Rips filtration
DTSTART:20240618T140000Z
DTEND:20240618T160000Z
DTSTAMP:20240806T212900Z
UID:indico-event-884@events.gwdg.de
DESCRIPTION:Speakers: Robert Tang\n\nGiven a metric space $X$ and a scale
parameter $\\sigma \\geq 0$\, the Rips graph $Rips^\\sigma X$ has $X$ as i
ts vertex set\, with two vertices declared adjacent whenever their distanc
e is at most $\\sigma$. A classical fact is that $X$ is a quasigeodesic sp
ace precisely if it is quasi-isometric to its Rips graph at sufficiently l
arge scale. By considering all possible scales\, we obtain a directed syst
em of graphs known as the Rips filtration. How does the large-scale geomet
ry of $Rips^\\sigma X$ evolve as $\\sigma \\to \\infty$? Is there a meanin
gful notion of limit? It turns out that the answers depends on whether we
work up to quasi-isometry or coarse equivalence. In this talk\, I will dis
cuss some results inspired by these questions.\n\nhttps://events.gwdg.de/e
vent/884/
LOCATION:SZ (MI)
URL:https://events.gwdg.de/event/884/
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