# On the moduli spaces of ALH*-gravitational instantons

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Gravitational instantons are defined as non-compact hyperKahler

4-manifolds with L^2 curvature decay. They are all bubbling limits of K3

surfaces and thus serve as stepping stones for understanding the K3 metrics.

In this talk, we will focus on a special kind of them called

ALH*-gravitational instantons. We will explain the Torelli theorem, describe

their moduli spaces and some partial compactifications of the moduli spaces.

This talk is based on joint works with T. Collins, A. Jacob, R. Takahashi,

X. Zhu and S. Soundararajan.

Earlier time and joint seminar with Differential Geometry Seminar.