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SUMMARY:Felix Schlenk (Université de Neuchâtel)
DTSTART:20211012T153000Z
DTEND:20211012T163000Z
DTSTAMP:20260423T022742Z
UID:Geolis/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/58/">
 On the group of symplectomorphisms of starshaped domains</a>\nby Felix Sch
 lenk (Université de Neuchâtel) as part of Geometria em Lisboa (IST)\n\n\
 nAbstract\nTake a simply connected compact domain $K$ in $\\mathbb R^{2n}$
  with smooth boundary. We study the topology of the group $\\mathrm{Symp} 
 (K)$ of those symplectomorphisms of $K$ that are defined on a neighbourhoo
 d of $K$. A main tool is a Serre fibration $\\mathrm{Symp} (K) \\to \\math
 rm{SCont} (\\partial K)$ to the group of strict contactomorphisms of the b
 oundary. The fiber is contractible if $K$ is 4-dimensional and starshaped\
 , by Gromov's theorem. The topology (or at least the connectivity) of the 
 group $\\mathrm{SCont} (\\partial K)$ can be understood in many examples. 
 In case this group is connected\, so is $\\mathrm{Symp} (K)$. This has app
 lications to the problem of understanding the topology of the space of sym
 plectic embeddings of $K$ into any symplectic manifold. If $\\mathrm{Symp}
  (K)$ is connected\, then for embeddings that are not related by an ambien
 t symplectomorphism there is not even an ambient symplectomorphism that ma
 ps one image to the other. \n\nThe talk is based on work with Joé Brendel
  and Grisha Mikhalkin.\n
LOCATION:https://researchseminars.org/talk/Geolis/58/
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