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SUMMARY:Dan Cristofaro-Gardiner (IAS and UC Santa Cruz): The Kapovich-Polt
erovich question
DTSTART;VALUE=DATE-TIME:20210518T143000Z
DTEND;VALUE=DATE-TIME:20210518T152000Z
DTSTAMP;VALUE=DATE-TIME:20220924T153700Z
UID:indico-contribution-5351@indico.math.cnrs.fr
DESCRIPTION:The group of Hamiltonian diffeomorphisms of a symplectic manif
old admits a remarkable bi-invariant metric\, called Hofer’s metric. Ma
ny basic questions about the geometry of this metric remain open. For exa
mple\, in 2006 Kapovich and Polterovich asked whether or not this group\,
in the case of the two-sphere\, is quasi-isometric to the real line. I wi
ll explain joint work with Humilière and Seyfaddini resolving this questi
on: we show that the group contains quasi-isometric copies of R^n for any
n\, and we also show that the group is not coarsely proper. Key to our pr
oofs is a new sequence of spectral invariants defined via Hutchings’ Per
iodic Floer Homology.\n\nhttps://indico.math.cnrs.fr/event/5787/contributi
ons/5351/
LOCATION:ZOOM (En ligne)
RELATED-TO:indico-event-5787@indico.math.cnrs.fr
URL:https://indico.math.cnrs.fr/event/5787/contributions/5351/
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