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Tea time：15:30, Room 707
Abstract:
The Gross-Siebert program is usually referred as the algebraic version of the famous SYZ mirror symmetry. The fundamental tool in their program is tropical geometry. A natural question that we want to address is how can one understand homological mirror symmetry under the framework of the Gross-Siebert program. In this talk, I am going to introduce the notion of tropical Lagrangian multi-sections, which is a combinatorial replacement of Lagrangian multi-sections in the SYZ proposal. Such tropical object can be used to construct locally free shaves on log Calabi-Yau varieties. I will discuss the existence and smoothabililty of these locally free sheaves and their relation to mirror symmetry.
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