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SUMMARY:Examples of tropical-to-Lagrangian correspondence - Grigory Mikhal
 kin\, University of Geneva
DTSTART:20180509T131500Z
DTEND:20180509T141500Z
UID:TALK98710@talks.cam.ac.uk
CONTACT:Mark Gross
DESCRIPTION:According to SYZ philosophy the same tropical object\nshould a
 dmit two ways to be lifted classically: as a\ncomplex object\, and as a (T
 -dual) symplectic object.\nWhile the tropical-to-complex correspondence is
 \nrelatively well-studied\, tropical-to-symplectic\ncorrespondence remains
  significantly less well-studied\nup to date.\n\nIn the talk we'll look at
  some first instances of tropical-\nto-symplectic correspondence. As an ap
 plication of such\ncorrespondence in the case of planar tropical curves we
 'll\nreprove a theorem of Givental (from about 30 years ago)\non Lagrangia
 n embeddings of connected sums of Klein\nbottles to C^2. For tropical curv
 es in toric 3-folds the resulting\nLagrangians turn out to be Waldhausen g
 raph-manifolds.\nFor this case we'll relate the enumerative multiplicity o
 f\ntropical rational curves  to the torsion in the first homology\ngroup o
 f the corresponding Lagrangian submanifolds\n(in full compliance with Mirr
 or Symmetry predictions).
LOCATION:CMS MR13
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