On a formulation of Strominger-Yau-Zaslow conjecture
演讲者
时间
2024年09月10日 15:00 至 16:00
地点
A7-101
线上
Zoom 638 227 8222
(BIMSA)
摘要
Given a graded or special Lagrangian fibration, we propose that the dual torus fibration, for a refined formulation of the SYZ conjecture, should be interpreted as a non-Archimedean torus fibration defined over the Novikov field. This proposal stems from a toy model of the SYZ duality, drawing parallels between the complex logarithm map and the non-Archimedean tropicalization map. Both are viewed as torus fibrations over Euclidean space, equipped with the trivial integral affine structure. A canonical globalization of this toy model, which preserves the integral affine structure, is constructed via (family) Floer theory applied to the family of Lagrangian fibers. Time permitting, we will briefly explain some basic aspects of non-archimedean geometry and/or explore explicit SYZ examples with extensions to singular fibers.