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SUMMARY:Nathaniel Bottman (University of Southern California)
DTSTART:20200811T200000Z
DTEND:20200811T210000Z
DTSTAMP:20260423T004757Z
UID:operad/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/operad/10/">
 The relative 2-operad of 2-associahedra in symplectic geometry</a>\nby Nat
 haniel Bottman (University of Southern California) as part of operad pop-u
 p\n\n\nAbstract\nThe Fukaya A-infinity category $\\mathrm{Fuk}(M)$ is a ri
 ch invariant of a symplectic manifold $M$\, and its manipulation and compu
 tation is a core focus of current symplectic geometry. Building on work of
  Wehrheim and Woodward\, I have proposed that the correct way to encode th
 e functoriality properties of $\\mathrm{Fuk}$ is by defining an "$(A_\\inf
 ty\,2)$-category" called Symp\, in which the objects are symplectic manifo
 lds and hom($M\,N$) is defined to be $\\mathrm{Fuk}(M^-\\times N)$. Underl
 ying the new notion of an $(A_\\infty\,2)$-category is a family of abstrac
 t polytopes called 2-associahedra\, which form a "relative 2-operad" (anot
 her new notion\, which is related to Batanin's theory of higher operads). 
 I will describe all of these constructions from scratch\, without assuming
  any knowledge of symplectic geometry. This talk is based partly on joint 
 work with Shachar Carmeli\, and I will mention related joint work with Ale
 xei Oblomkov.\n
LOCATION:https://researchseminars.org/talk/operad/10/
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