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SUMMARY:Pranav Chakravarthy (Hebrew University of Jerusalem)
DTSTART:20220323T121000Z
DTEND:20220323T133000Z
DTSTAMP:20260423T005715Z
UID:GDS/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDS/51/">Hom
 otopy type of equivariant symplectomorphisms of rational ruled surfaces</a
 >\nby Pranav Chakravarthy (Hebrew University of Jerusalem) as part of Geom
 etry and Dynamics seminar\n\n\nAbstract\nIn this talk\, we present results
  on the homotopy type of the group of \nequivariant symplectomorphisms of 
 $S^2 \\times S^2$ and $\\mathbb{C}P^2$ blown \nup once\,  under the presen
 ce of Hamiltonian group actions of either $S^1$ or \nfinite cyclic groups.
  For  Hamiltonian circle actions\, we prove that the \ncentralizers are ho
 motopy equivalent to either a torus or to the homotopy \npushout of two to
 ri depending on whether the circle action extends to a single \ntoric acti
 on or to exactly two non-equivalent toric actions. We can show that \nthe 
 same holds for the centralizers of most finite cyclic groups in the \nHami
 ltonian group. Our results rely on J-holomorphic techniques\, on Delzant's
  \nclassification of toric actions\, on Karshon's classification of Hamilt
 onian \ncircle actions on 4-manifolds\, and on the Chen-Wilczy\\'nski smoo
 th \nclassification of $\\mathbb{Z}_n$-actions on Hirzebruch surfaces.\n
LOCATION:https://researchseminars.org/talk/GDS/51/
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