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Explore an advanced mathematics lecture delving into the algebraic-geometric perspective of SYZ dual torus fibrations in mirror symmetry. Learn about the joint program with Mark Gross that constructs mirror dual degenerating families with central fibers unions of toric varieties through wall structures. Discover how wall structures are defined to construct mirror toric degenerations via Gromov-Witten theory in general Calabi-Yau geometries, demonstrating intrinsic mirror symmetry. Understand how this approach provides an algebraic-geometric implementation of quantum corrections to the complex structure of the mirror SYZ fibration, bridging both differential-geometric and non-archimedean frameworks.
