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SUMMARY:Chris Brav (Higher School of Economics\, Moscow\, Russia)
DTSTART:20221124T120000Z
DTEND:20221124T130000Z
DTSTAMP:20260423T005756Z
UID:LAGOON/79
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LAGOON/79/">
 Poisson brackets and the string Lie algebra of a Calabi-Yau category</a>\n
 by Chris Brav (Higher School of Economics\, Moscow\, Russia) as part of Lo
 ngitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract
 \nGoldman defined a symplectic structure on the moduli space of local syst
 ems on a closed oriented surface\, constructed a collection of natural Ham
 iltonians on the moduli space by taking trace of monodromy around loops on
  the surface\, and computed Poisson brackets among these Hamiltonians in t
 erms of what is now called the Goldman bracket on free homotopy classes of
  loops. Chas and Sullivan generalized the Goldman bracket to a string brac
 ket on the degree-shifted equivariant homology of the free loop space of a
  closed oriented manifold of any dimension\, but the compatibility with th
 e corresponding shifted-symplectic geometry on the moduli space of local s
 ystems remained mostly conjectural. We generalize these results of Goldman
  and of Chas-Sullivan to higher dimensional ’non-commutative’ closed o
 riented manifolds in the form of smooth Calabi-Yau categories. Our main re
 sults are the description of a chain-level ’string Lie bracket’ on cyc
 lic chains of a smooth Calabi-Yau category and the intertwining of this st
 ring Lie bracket on cyclic chains with the shifted Poisson bracket on func
 tions on the moduli space of objects in the category.\n\nMeeting Link\n\nh
 ttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz0
 9\n\nMeeting ID: 918 7552 8987 Password: LAGOON2022\n
LOCATION:https://researchseminars.org/talk/LAGOON/79/
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