Special Lagrangian submanifolds from tropical-like data

Abstract: Special Lagrangian submanifolds are volume-minimizing Lagrangians in Calabi-Yau manifolds. Their existence not only provides a rich source of higher-codimensional minimal submanifolds, but also plays a central role in the SYZ picture of mirror symmetry. However, existence results remain scarce, especially in the compact case. In this talk, I will present two gluing constructions: (1) special Lagrangians in K3-fibered Calabi-Yau 3-folds, and (2) special Lagrangians in the simplest SYZ fibration, $T^*T^n$. In both cases, the starting point is a tropical-like graph in the base of the fibration, which guides the gluing of local models. Based on joint works with Yang Li and Yu-Shen Lin.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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