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Explore the construction of Lagrangian torus fibrations on Calabi-Yau hypersurfaces in toric Fano manifolds through this 53-minute conference talk. Discover joint work with Mak-Ruddat-Zharkov that proves the existence of these fibrations on Calabi-Yau hypersurfaces given by reflexive polytopes, motivated by the Strominger-Yau-Zaslow conjecture which predicts such fibrations near large complex structure limits. Learn about the innovative approach that replaces ordinary algebraic equations with new formulations involving "ironing coefficients" and convex potentials to break manifolds into local models. Understand how the Liouville flow technique in the style of Evans-Mauri is applied over these models to achieve the construction. Gain insights into advanced topics in algebraic geometry and singularity theory from this presentation delivered at the "New Developments in Singularity Theory" conference at the University of Miami.
