3:30 pm Thursday, May 2, 2013
Geometry Seminar: On the symplectic cohomology of log Calabi-Yau surfaces by
James Pascaleff [mail] (University of Texas at Austin) in RLM 9.166
Log Calabi-Yau manifolds (the complement Y-D of an effective anticanonical divisor D in a projective manifold Y) have a rich symplectic geometry. They are the subject of a mirror symmetry conjecture: roughly, if Y-D is affine, there is a mirror variety M, that is also affine log Calabi-Yau, and the Floer theory of Y-D is reflected in the algebraic geometry of M. For instance, one expects to find the ring of regular functions on M sitting inside the symplectic cohomology of Y-D. I will describe some results towards this conjecture, in complex dimension two. There is a basis for degree zero symplectic cohomology indexed by integral points in a certain SL(2,Z)-manifold (related to the Gross-Hacking-Keel theta functions). We can also compute the product structure in a particular case. Submitted by
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