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For questions about Fukaya categories (as introduced by Fukaya in 1993) and their structure; consider also related tags such as [floer-homology] or [lagrangian-submanifolds].
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Mirror symmetry for singular Lagrangian torus fibrations
Yes, there is a concrete program on how to handle singular fibers in the SYZ fibration and several steps of this program are already completed.
You can watch the videos of Abouzaid lectures on the su …