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SUMMARY:Jeff Hicks (Edinburgh)
DTSTART:20220407T090000Z
DTEND:20220407T100000Z
DTSTAMP:20260423T005800Z
UID:notts_ag/98
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/notts_ag/98/
 ">Realizing tropical curves via mirror symmetry</a>\nby Jeff Hicks (Edinbu
 rgh) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract
 \nThe tropicalization map associates to each curve in the algebraic n-toru
 s a piecewise linear object (tropical curve) in real n-dimensional space. 
 Given a tropical curve\, a natural question is if it can arise as the trop
 icalization of some algebraic curve. If this is the case we say that the t
 ropical curve is realizable. Determining good realizability criteria for t
 ropical curves remains an important part of tropical geometry since Mikhal
 kin provided examples of non-realizable tropical curves. We explore the fo
 llowing strategy for realizing tropical curves:\n(1) Produce a Lagrangian 
 submanifold of the cotangent bundle of the torus whose moment map projecti
 on approximates the tropical curve\;\n(2) Use homological mirror symmetry 
 to obtain a mirror algebraic sheaf\;\n(3) Show that the tropicalization of
  the support of this sheaf is the original tropical curve.\nWe will give f
 ull answers to (1) and (3)\, and explain why (2) is fairly subtle. As appl
 ications\, we will obtain some new and known realizability statements for 
 tropical curves.\n
LOCATION:https://researchseminars.org/talk/notts_ag/98/
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