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Explore the metric behavior of Calabi-Yau metrics on fibrations through this differential geometry and physics seminar lecture by Gabor Szekelyhidi from Northwestern University. Delve into the well-studied problem of understanding how Calabi-Yau metrics behave in families of Kähler classes that collapse the fibers of a fibration. Learn about recent progress demonstrating that the Gromov-Hausdorff limit can be identified with the base of the fibration, building upon and generalizing important results from Gross-Tosatti-Zhang, Song-Tian-Zhang, and Li-Tosatti. Discover how exploiting the RCD (Riemannian Curvature-Dimension) property of the Gromov-Hausdorff limit serves as a crucial new ingredient in this analysis. Gain insights into advanced topics in differential geometry, complex geometry, and mathematical physics through this detailed examination of collapsing Calabi-Yau fibrations and their geometric limits.
