Analysis Seminar

Ruobing ZhangStony Brook University
Geometric analysis of collapsing Calabi-Yau spaces

Monday, September 16, 2019 - 2:30pm
Malott 406

In this talk, we focus on the collapsing behaviors of Calabi-Yau metrics on a degenerating family of Calabi-Yau manifolds. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties and highly non-algebraic features. As motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. We will analyze in details the bubbling behaviors and the metric-measure geometry in various contexts. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of Calabi-Yau metrics which limit to a closed interval. Such constructions enable us to accurately and explicitly characterize how complex structures degenerate from the metric geometric point of view.