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SUMMARY:Brent Pym (McGill University)
DTSTART:20210422T200000Z
DTEND:20210422T210000Z
DTSTAMP:20260423T021235Z
UID:SGFM/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SGFM/19/">A 
 global Weinstein splitting theorem for holomorphic Poisson manifolds.</a>\
 nby Brent Pym (McGill University) as part of Seminario de Geometría y Fí
 sica - Matemática UCN-USP\n\n\nAbstract\nA foundational result in Poisson
  geometry\, due to Weinstein\,\nstates that any Poisson bracket on a manif
 old can be written locally as\nthe Poisson bracket of symplectic form in c
 anonical coordinates\, and a\nPoisson bracket that vanishes at a point.  
 A key consequence is that\nevery Poisson manifold has a canonical foliatio
 n with symplectic leaves.\nI will give an introduction to these ideas\, an
 d then discuss the problem\nof globalizing Weinstein's decomposition\, to 
 split the manifold itself\n(or a covering thereof) as a product of a sympl
 ectic leaf and a\ntransverse Poisson manifold.  While the existence of su
 ch a splitting is\nrare in the context of smooth manifolds\, it turns out 
 to be automatic\nfor holomorphic Poisson structures on compact Kähler man
 ifold admitting\na simply-connected compact symplectic leaf.  This talk i
 s based on joint\nwork with Stéphane Druel\, Jorge Vitório Pereira\, and
  Frédéric Touzet\,\nwhich in turn relies in an essential way on a notion
  of "subcalibrations"\nin Poisson geometry introduced recently by Pedro Fr
 ejlich and Ioan Mărcuț.\n
LOCATION:https://researchseminars.org/talk/SGFM/19/
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