地点：数学高等研究院报告厅

报告人：Charlie Cifarelli (Stony Brook University)

摘要: Since Calabi's original paper, the Calabi Ansatz has been central for constructions in Kähler geometry. Calabi himself used it to construct complete Ricci-flat metrics on the total space of the canonical bundle of a Kähler-Einstein Fano manifold B, generalizing some well-known examples coming from physics. Over the years, work of Koiso, Cao, Feldman-Ilmanen-Knopf, Futaki-Wang, Chi Li, and others have shown that the Calabi Ansatz can be used to produce complete Kähler-Ricci solitons, important singularity models for the Kähler-Ricci flow, on certain line bundles over B. In this talk, I'll explain a generalization of these results to the total space of some higher-rank direct-sum vector bundles over B. In our case the Calabi Ansatz is not suitable, and we instead use the theory of hamiltonian 2-forms, introduced by Apostolov-Calderbank-Gauduchon-Tønneson-Friedman. The construction produces new examples of complete shrinkers, steadies, and Calabi-Yau metrics, and unifies the aforementioned results using Calabi Anzatz with previous constructions of the author and Apostolov and of Martelli-Sparks.