Abstract: Gravitational instantons are non-compact Calabi-Yau metrics with L^2 bounded curvature and are categorized into six types. I will describe several projects on gravitational instantons including: Fredholm theory and deformation, non-collapsing degeneration limits, and existence of stable non-holomorphic minimal spheres in certain types. These projects utilize geometric microlocal analysis in different settings, where the analysis of singular operators is obtained through geometric resolutions. Based on works jointly with Rafe Mazzeo, Yu-Shen Lin, Sidharth Soundararajan, and Alia Yusaini.

Brief biography: Xuwen Zhu is currently an associate professor at Northeastern University. She obtained her Ph.D. at MIT in 2015 under the supervision of Richard Melrose. Her research focuses on microlocal analysis and differential geometry.

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