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Special seminar: SYZ fibrations and tropical geometry

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If you have a question about this talk, please contact Ailsa Keating .

The Strominger-Yau-Zaslow conjecture proposes that “mirror pairs” (pairs of spaces whose symplectic and complex invariants are interchanged) can be constructed by considering dual Lagrangian torus fibrations. In this introductory talk, we will demonstrate how to build dual Lagrangian torus fibrations from the data of an affine manifold. I’ll also discuss how to lift affine subspaces to complex and Lagrangian submanifolds and perform some sample computations that motivate Kontsevich’s homological mirror symmetry conjecture. Finally, I’ll state some theorems illustrating how symplectic geometry can be applied to algebraic geometry.

This talk is part of the Differential Geometry and Topology Seminar series.

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