Tropical Lagrangians and mirror symmetry

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• Jeff Hicks, Berkeley & ETH
• Wednesday 21 November 2018, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

Homological mirror symmetry predicts that the Fukaya category of a symplectic manifold X can be matched with the derived category of coherent sheaves on a mirror space Y. The Strominger-Yau-Zaslow conjecture states that X and Y should have dual Lagrangian torus fibrations, and that mirror symmetry can be recovered by reducing the symplectic and complex geometry of X and Y to tropical geometry on the base of the fibration. In this framework, we expect that Lagrangian fibers of X are mirror to skyscraper sheaves of points on Y, and that Lagrangian sections of the fibration are mirror to line bundles on Y. I will explain how to extend these correspondences to tropical Lagrangians in X and sheaves supported on cycles of intermediate dimension on toric varieties.

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

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