**u`Ό pκwζ[u`iw4jiLecture on Advanced Science in English@iMathematics 4)j@@ΘΪR[hFZUA.E347
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S Jeff Viaclovsky@ΑC³φ
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@Kahler manifolds, Ricci curvature, and hyperkahler
metrics

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@In these lectures, we will begin with a review of some basics of Kahler geometry and the curvature of Kahler metrics.
We will then focus on the Ricci-flat case, and discuss some details of K3 surfaces.
We will also consider complete noncompact examples of hyperkahler metrics, and relations with the Gibbons-Hawking ansatz.
We will then give some details of the author's recent work with Hein, Sun, and Zhang, which constructs collapsing sequences of Ricci-flat metrics
on the K3 surface with nontrivial nilpotent collapsing structure.