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Explore an advanced mathematics lecture delving into algebraic-geometric perspectives on SYZ dual torus fibrations in mirror symmetry. Learn about the joint program with Mark Gross that constructs mirror dual degenerating families through wall structures and toric varieties. 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 mirror SYZ fibration, bridging both differential-geometric and non-archimedean frameworks.
