Geometric analysis of collapsing Calabi-Yau spaces
This talk centers on the degenerations of Calabi-Yau manifolds. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsed contexts. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties and highly non-algebraic features.
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in much broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.