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DTSTART:20250309T070000
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DTSTART;TZID=America/Toronto:20251121T153000
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URL:https://uwaterloo.ca/pure-mathematics/events/geometry-and-topology-semi
 nar-40
SUMMARY:Geometry and Topology Seminar
CLASS:PUBLIC
DESCRIPTION:SIYUAN YU\, WESTERN UNIVERSITY\n\n_Symplectic embeddings of bal
 ls in __ℂ__P__²__ and the generalized\nconfiguration space_\n\nLet IEmb
 (B⁴(c)\,ℂP²) denote the space of unparameterized\nsymplectic embeddin
 gs of k balls of capacities (c₁\,...\,cₖ)\, where\n1 ≤ k ≤ 8. It i
 s known from the work of S. Anjos\, J. Li\, T.-J. Li\,\nand M. Pinsonnault
  that the space of capacities decomposes into convex\npolygons called stab
 ility chambers\, and that the homotopy type of\nIEmb(B⁴(c)\,ℂP²) depe
 nds solely on the stability chambers. Based\non recent results of M. Entov
  and M. Verbitsky on Kähler-type\nembeddings\, we show that for 1 ≤ k 
 ≤ 8\, IEmb(B⁴(c)\,ℂP²) is\nhomotopy equivalent to a union of strata
  F_I of the configuration\nspace of the complex projective plane F(ℂP²\
 ,k). The proof relies on\nconstructing an explicit map from the space of K
 ähler type embeddings\nto a generalized version of the configuration spac
 e that incorporates\nboth configurations of points and compatible complex 
 structures on\nℂP².\n\nMC 5417
DTSTAMP:20260504T180044Z
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