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New Special Lagrangians in Calabi-Yau 3-folds with K3-Fibrations


Speaker: Yu-Shen Lin, Boston University
Location: 2112 MSB
Start time: Tue, Jan 9 2024, 2:10PM

Special Lagrangians are an important class of minimal submanifolds in Calabi-Yau manifolds. The special Lagrangian tori are the building block of the Strominger-Yau-Zaslow conjecture and plays the crucial role of reconstructing mirrors Calabi-Yau manifolds. Special Lagrangians are conjecturally the stable objects in the Fukaya category and their counting is mirror to the Donaldson-Thomas invariants in algebraic geometry, which count semi-stable sheaves. However, very little examples of special Lagrangians are known. In this talk, I will explain a gluing construction of special Lagrangian spheres in Calabi-Yau 3-folds with K3-fibrations. Gromov-Hausdorff converges to a curve on the base as the K3-fibres collapse and can be viewed as a tropicalization process for special Lagrangians. If the time permits, I will also explain the relation with Thomas-Yau conjecture. This is a joint work with Shih-Kai Chiu.