Noncommutative Geometry Seminar
Date: February 22, 2023
Time: 4:00PM - 5:00PM
Location: BLOC 628
Speaker: Ruobing Zhang, Princeton University
Title: (Joint with Topology Seminar) Metric geometry of Einstein 4-manifolds with special holonomy
Abstract: Studying the geometry of Einstein spaces and their generalizations is a major theme in current areas of differential geometry. This talk will introduce major developments in the metric geometry and global analysis of Einstein 4-manifolds. Recently geometric studies have culminated in a complete understanding of Einstein 4-manifolds with special holonomy.
Among the tremendous progress in this area, an essential chapter is to understand how Einstein moduli spaces can be compactified and how Einstein metrics can degenerate, especially when volume collapse occurs. Understanding collapsing geometry is much more challenging than studying the non-collapsing case so that little progress was made during the past three decades. I will particularly summarize recent breakthrough in this direction on the accurate characterization of singularity formation and the complete classification of degeneration limits on all scales.