Local mirror symmetry in the tropics
Mark Gross (Cambridge, U.K.)
What 


When 
Apr 24, 2014 from 03:15 pm to 04:15 pm 
Where  Mainz, 05432 (Hilbertraum) 
Contact Name  Helge Ruddat 
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We discuss how the
GrossSiebert reconstruction theorem applies to the local mirror symmetry of
Chiang, Klemm, Yau and Zaslow. The reconstruction theorem associates to certain
combinatorial data a degeneration of (log) CalabiYau varieties. While in this
case most of the subtleties of the construction are absent, an important
normalization condition already introduces rich geometry. This condition
guarantees the parameters of the construction are canonical coordinates in the
sense of mirror symmetry. The normalization condition is also related to a
count of holomorphic disks and cylinders, as conjectured in our work and
partially proved in various works of Chan, Cho, Lau, Leung and Tseng. We sketch
a possible alternative proof of these counts via logarithmic GromovWitten
theory.
There is also a surprisingly simple interpretation via rooted trees marked by
monomials, which points to an underlying rich algebraic structure both in the
relevant period integrals and the counting of holomorphic disks