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SUMMARY:Defining Fukaya Categories Geometrically - Daniil Mamaev\, London 
 School of Geometry and Number Theory
DTSTART:20250314T160000Z
DTEND:20250314T170000Z
UID:TALK225637@talks.cam.ac.uk
CONTACT:Adrian Dawid
DESCRIPTION:I will outline a construction of a triangulated Fukaya categor
 y directly from geometric data in the case of relative wrapped Fukaya cate
 gories of surfaces. These pop up in two ways. One is in homological mirror
  symmetry\, where they allow to interpret braid group actions on derived c
 ategories as mapping class group actions. Another\, conjectured by Lekili-
 Segal\, is that they are equivalent to wrapped Fukaya categories of higher
 -dimensional symplectic manifolds admitting certain algebraic torus fibrat
 ions.\n\nThe construction is explicit\, meaning that all objects of the ca
 tegory are just curves with additional data\, and does not involve any cho
 ices such as a coherent perturbation scheme. The key ingredients to achiev
 e that are to work with a version of a Chekanov-Eliashberg algebra of a Le
 gendrian lift of a curve in the surface as obstruction algebra and with A-
 infinity pre-categories.\n\nI will explain\, without assuming familiarity 
 with Fukaya categories\, what the objects\, morphisms\, and A-infinity ope
 rations in a relative wrapped Fukaya category of surface are\, why it is t
 riangulated\, what the correct notion of isotopy invariance in this contex
 t is\, and how to find finitely many curves that generate the category. 
LOCATION:MR13
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