Northwestern-UIC Complex Geometry Seminar

Abstract: I will present a recent joint work with D.H. Phong, J. Song and J. Sturm on the diameter estimate and noncollapsing for Kahler metrics, which are uniform in a bounded set of the Kahler metrics and require only certain integral bound of the volume form, and no assumptions on Ricci curvature are needed.  As applications, diameter bounds are obtained for long-time solutions of the Kähler-Ricci flow and finite-time solutions when the limit class is big.

Abstract: This talk concerns some recent progress in understanding the collapsing geometry of Calabi-Yau manifolds. Particularly in the case of complex dimension two, together with my collaborators, we obtained an essentially complete picture on the degenerations of the Calabi-Yau metrics on all scales.