中科院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
调和分析和偏微分方程研讨班
报告人：Xuwen Zhu（Northeastern University）
题 目：Analysis and degeneration of gravitational instantons
时 间：2024.07.23（星期二）16:00-17:00
地 点：思源楼S813
摘 要：Gravitational instantons are non-compact Calabi-Yau metrics with L^2 bounded curvature and are categorized into six types. We will focus on one such type called ALH* metrics which has a non-compact end with inhomogeneous collapsing near infinity. Such metrics appeared recently in the works on SYZ conjecture, as well as the scaling bubble limits for codimension-3 collapsing of K3 surfaces. I will talk about a joint project with Rafe Mazzeo on the Fredholm mapping property and L^2 cohomology of ALH* metrics, where the geometric microlocal analysis of fibered metrics plays a central role. I will also discuss the joint work with Yu-Shen Lin and Sidharth Soundararajan on the degeneration of such metrics which gives a partial compactification of their moduli space.
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