Venue: Lecture Hall of IASM

Time: 14:30-15:30, July 7, Monday

Speaker: Xuwen Zhu 朱煦雯 (Northeastern University)

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 joint with Rafe Mazzeo, Yu-Shen Lin and Sidharth Soundararajan.