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SUMMARY:Boris Zupancic (McGill University)
DTSTART:20261002T150000Z
DTEND:20261002T161500Z
DTSTAMP:20261025T111745Z
UID:CIRGET/169
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CIRGET/169/"
 >Reduction of singularities in Poisson geometry via weighted blowups</a>\n
 by Boris Zupancic (McGill University) as part of CRM - Séminaire du CIRGE
 T / Géométrie et Topologie\n\nLecture held in PK-5115.\n\nAbstract\nHiro
 naka’s theorem on resolution of singularities via\nblowups fails in Pois
 son geometry\, since blowups generally destroy\nPoisson structures. Howeve
 r\, there exists a more general operation\ncalled a weighted blowup\, whic
 h may provide a viable alternative. Weighted blowups have proven useful in
  the recent literature\non resolution of singularities\; for instance\, in
  the non-Poisson setting\, Abramovich-Temkin-Wlodarczyk have shown that fa
 st functorial resolution of singularities can always be achieved by seque
 ntially blowing up the worst singularities via a canonical choice of\nweig
 hted blowup. We take a similar approach to show that appropriate choices o
 f weighted blowups produce reduction of singularities in low-dimensional 
 Poisson geometry. In joint work with\nSimon Lapointe\, Mykola Matviichuk a
 nd Brent Pym\, we obtain:\n(1) a criterion for lifting a Poisson structure
  to a weighted blowup\,\n(2) a classification of normal forms of Poisson v
 arieties not admitting any weighted blowup\, in low-dimension\, and (3) a 
 theorem on\nthe extent to which weighted blowups can reduce the singularit
 ies\nof Poisson varieties\, in low-dimension.\n
LOCATION:https://researchseminars.org/talk/CIRGET/169/
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