Seminar| Institute of Mathematical Sciences
Time：14:00-16:00, June 18, Tuesday
Location：Room S407, IMS
Speaker: Ruobing Zhang, IMS
Abstract: This talk focuses on recent progress regarding the collapsing theory of Einstein spaces. Specifically, the talk consists of the following primary parts:
(1) We will introduce some regularity and structure theorems for higher dimensional collapsing manifolds with Ricci curvature bounds which works in very general settings.
(2) This talk is also concerned with the geometry of collapsed Ricci-flat Kähler manifolds. Besides exhibiting new collapsing Einstein families, we will establish the correspondence between complex structures (Type II) degeneration and the metric collapsing.
(3) We will construct new families of collapsed Einstein metrics in low dimensions, especially for K3 manifolds. This part involves producing new bubble limits, constructing singular nilpotent Killing structures and understanding multi-scale collapsing with singularities.