Lagrangian submanifolds in almost toric fibrations

Abstract: Mirror symmetry predicts that Lagrangian submanifolds of a symplectic space X are mirror to coherent sheaves on a ``mirror space'' Y. A proposed mechanism for mirror symmetry comes from almost Lagrangian torus fibrations. In this framework, X and Y are dual Lagrangian torus fibrations over a common affine base Q. Mirror symmetry arises by degenerating the symplectic geometry of X and complex geometry of Y to tropical geometry on the base Q. We will look at the setting where X is the complement of the elliptic curve in the projective plane, and discuss how to construct Lagrangian submanifolds of X from the data of tropical curves in the base of the fibration.

algebraic geometrydifferential geometryquantum algebrasymplectic geometry

Audience: researchers in the topic

Boston University Geometry/Physics Seminar

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