Moduli Space of ALH^*-Gravitational Instantons


Yu-Shen Lin (Boston University, USA)
2022-12-27  10:00 - 11:30
Room 202, Astronomy and Mathematics Building

Gravitational instantons are non-compact complete hyperK\"ahler 4-manifolds with L2-curvature. They are known to be the bubbling limits of K3 surfaces. Thus can be viewed as the "non-compact K3" and the building block toward understanding K3 metrics. Similar to the K3 surfaces case, the cohomology classes of the hyperK\"ahler triples of gravitational instanton determine the period map. In this talk, I will show that the period map is a diffeomorphism for a class of gravitational instantons, labeled by ALH*. If time permits, I will explain the work in progress on the boundary of the moduli space. The talk is based on the series of joint works with Collins, Jacob, Lee, Zhu, Soundararaja and Takahashi.