中科院数学与系统科学研究院

数学研究所

学术报告

几何拓扑研讨班

报告人张若冰(普林斯顿大学)

 Metric geometry of Einstein spaces

  2022.08.17(星期三)08:30-09:30

 点:腾讯会议:145-848-869/N219

 要:This talk centers around recent major developments in the degeneration theory and quantitative analysis of Einstein metrics. In the volume non-collapse setting, a complete degeneration picture has been well established during the past three decades, and its profound applications have been well appreciated. However, the metric geometry of collapsing Einstein manifolds is less explored, and little is known in any general context. A fundamental reason is that most tools from geometric analysis legitimately fail when the spaces are collapsing.

The main part of this talk surveys my investigations on the collapsing geometry of Einstein metrics with special holonomy, particularly the Calabi-Yau geometry. Together with my collaborators, our recent results with creations of new tools provide a rather complete profile of complex 2D Calabi-Yau spaces in the collapsing context: metric geometries at all scales have been completely well understood. This can be viewed as a preliminary step of making progress in understanding general Einstein metrics.

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