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SUMMARY:Tropical Lagrangians and mirror symmetry - Jeff Hicks\, Berkeley &
 amp\; ETH
DTSTART:20181121T160000Z
DTEND:20181121T170000Z
UID:TALK109060@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:Homological mirror symmetry predicts that the Fukaya category 
 of a symplectic manifold X can be matched with the derived category of coh
 erent sheaves on a mirror space Y. The Strominger-Yau-Zaslow conjecture st
 ates that X and Y should have dual Lagrangian torus fibrations\, and that 
 mirror symmetry can be recovered by reducing the symplectic and complex ge
 ometry of X and Y to tropical geometry on the base of the fibration. In th
 is framework\, we expect that Lagrangian fibers of X are mirror to skyscra
 per sheaves of points on Y\, and that Lagrangian sections of the fibration
  are mirror to line bundles on Y. I will explain how to extend these corre
 spondences to tropical Lagrangians in X and sheaves supported on cycles of
  intermediate dimension on toric varieties.
LOCATION:MR13
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