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Title: Collapsing geometry of Calabi-Yau metrics in complex dimension two

Speaker: 张若冰 （普林斯顿大学）

Abstract: Calabi-Yau metrics exhibit highly complicated behaviors as collapse occurs, which leads to substantial difficulties in both analytic and geometric aspects. Even in complex dimension two, singularity formation in the most generality was unknown prior to our work. In this talk we will establish a complete picture for the degeneration of Calabi-Yau metrics in complex dimension two (joint with Song Sun).

(1) Any collapsed limit of Calabi-Yau metrics on the K3 surface must be isometric to one of the following: a flat metric on the quotient of a flat 3D torus by an involution, a singular special Kaehler metric on the topological 2-sphere with nonnegative curvature in the Aleksandrov sense, or the unit interval.

(2) Any complete non-compact Calabi-Yau manifold with quadratically integrable curvature must have an asymptotic model end which can be compactified in a complex geometric sense, and hence all such manifolds are completely classified.

北京时间：2022年3月22日（周二）上午9:00—10:00
线上参加：#腾讯会议 834-644-125

联系人：张振雷

欢迎各位老师和同学们参加！