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Explore the intricacies of ALH* gravitational instantons in this comprehensive lecture from the International Conference on Birational Structures 2024. Delve into the world of non-compact Calabi-Yau metrics with L^2 bounded curvature, focusing specifically on ALH* metrics characterized by inhomogeneous collapsing near infinity. Examine the role of these metrics in recent works on the SYZ conjecture and scaling bubble limits for codimension-3 collapsing of K3 surfaces. Investigate the Fredholm mapping property and L^2 cohomology of ALH* metrics, and discover insights into the partial compactification of their moduli space. Learn about the degeneration limits involving ALH* and ALH gravitational instantons, based on ongoing collaborative projects with renowned mathematicians Rafe Mazzeo, Yu-Shen Lin, and Sidharth Soundararajan.
