Time：10:00-12:00, Wednesday, September 9 2026
Venue：E14-212
Host：Jiyuan Han, ITS
Speaker：Ruiming Liang, Peking University
Title：Construction of noncompact complete Calabi-Yau metrics
Abstract：In this talk, I will first briefly review the history of the construction of complete noncompact Calabi–Yau metrics. I will then explain my recent construction on K3 fibrations [1]. The main difficulty lies in the fact that the semi-Ricci-flat approximation at infinity provides an ansatz whose sectional curvature is not uniformly bounded. As a result, the traditional Tian–Yau–Hein package cannot be applied directly. The main strategy is to collapse the fiber and employ a global gluing construction, then develop an optimal linear theory for the collapsing ansatz. This enables us to apply the implicit function theorem between Banach spaces and perturb the ansatz into a genuine Calabi–Yau metric.
Reference: [1] Liang R. Complete Calabi-Yau metrics on noncompact K3 fibered threefolds[J]. arXiv preprint arXiv:2606.13011, 2026.
