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SUMMARY:Special seminar: Superabundance and Lagrangian submanifolds - Jeff
  Hicks (Edinburgh)
DTSTART:20241031T100000Z
DTEND:20241031T110000Z
UID:TALK222490@talks.cam.ac.uk
CONTACT:Ailsa Keating
DESCRIPTION:One version of the realizability problem asks\, "Which tropica
 l subvarieties can be lifted to algebraic subvarieties?" In his early work
  on the subject\, Mikhalkin exhibited a superabundant tropical curve that 
 could not be lifted to an algebraic variety. However\, in 2014\, Cheung\, 
 Fantini\, Park\, and Ulirsch showed that all trivalent tropical curves tha
 t are non-superabundant possess algebraic lifts.\n\nOn the mirror side\, e
 very trivalent tropical curve can be lifted to a Lagrangian submanifold! H
 owever\, these Lagrangian submanifolds may bound holomorphic disks (and th
 erefore be unsuitable for homological mirror symmetry). It is expected tha
 t the realizable tropical subvarieties have "unobstructed" Lagrangian subm
 anifold lifts—-in the sense that the counts of holomorphic disks cancel 
 out in homology. In this talk\, we'll show that the non-superabundance con
 dition implies the unobstructedness of the corresponding tropical Lagrangi
 an lift in dimension three.
LOCATION:MR13
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