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SUMMARY:A mirror symmetry conjecture - Michela Barbieri\, University Colle
 ge London
DTSTART:20231117T160000Z
DTEND:20231117T170000Z
UID:TALK204301@talks.cam.ac.uk
CONTACT:Alexis Marchand
DESCRIPTION:Anything about mirror symmetry refers to some mysterious relat
 ionships between complex and symplectic geometry. One form of it says that
  if you have some complex geometry X\, there is a mirror symplectic geomet
 ry Y such that (in some sense) the derived category of coherent sheaves on
  X\, denoted D^b(Coh X)\, is equivalent to the Fukaya category of Y\, deno
 ted Fuk(Y). \n\nIn fact\, starting from a complex geometry (think an algeb
 raic variety) there isn't just one mirror. There's a family of mirrors liv
 ing over a parameter space\, which is sometimes referred to as the Stringy
  Kähler Moduli Space (SKMS). The fundamental group of the SKMS acts natur
 ally on Fuk(Y) via monodromy\, and by mirror symmetry\, we expect to see t
 his action carry over. My goal is to explain some details of this story in
  the context of Calabi Yau toric geometric invariant theory\, where it's c
 onjectured that the fundamental group acts on the derived category via sph
 erical twists. We'll start by introducing the derived category\, geometric
  invariant theory\, and see where we get to!
LOCATION:MR13
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