Zoom link: https://princeton.zoom.us/j/594605776

This talk describes a complete picture on the collapsing geometry of hyperkaehler 4-manifolds. We will present the classifications of the collapsing limits, all the rescaling limits and singularity formations. As rescaling bubbles of degenerating hyperkaehler manifolds, gravitational instantons with finite energy will be completely classified. We will also introduce several applications based on the above classification results.