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SUMMARY:Ely Kerman (University of Illinois Urbana-Champaign)
DTSTART:20211123T163000Z
DTEND:20211123T173000Z
DTSTAMP:20260423T022620Z
UID:Geolis/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/63/">
 On symplectic capacities and their blind spots</a>\nby Ely Kerman (Univers
 ity of Illinois Urbana-Champaign) as part of Geometria em Lisboa (IST)\n\n
 \nAbstract\nIn this talk I will discuss a joint work with Yuanpu Liang in 
 which we establish some results concerning the symplectic capacities defin
 ed by Gutt and Hutchings using $S^1$-equivariant symplectic homology. Our 
 primary result settles a version of the recognition question in the negati
 ve. We prove that the Gutt-Hutchings capacities\, together with the volume
 \, do not constitute a complete set of symplectic invariants for star-shap
 ed (in fact convex) domains with smooth boundary. We also prove that\, eve
 n for star-shaped domains with smooth boundaries\, these capacities are mu
 tually independent and are independent from the volume. The constructions 
 that demonstrate these independence properties​ are not exotic. They are
  convex and concave toric domains. The new tool used here is a significant
  simplification of the formulae of Gutt and Hutchings for the capacities o
 f convex/concave toric domains\, that holds under an additional symmetry a
 ssumption. This allows us to identify new mutual blind spots of the capaci
 ties which are then used to construct the desired examples.\n
LOCATION:https://researchseminars.org/talk/Geolis/63/
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