002 Local regularities and singularities in Ricci flow

2021-03-12 10:32:45





报告题目:Four dimensional gradient Ricci solitons

报告摘要:Ricci solitons are important in the singularity analysis of Ricci flows. It is conjectured that the classification four-dimensional singularities models of compact Ricci flows can be reduced to the classification of four-dimensional shrinking and steady gradient Ricci solitons. In this talk, we will talk about some recent progress on the classification of shrinking and steady gradient Ricci solitons. Related conjectures and problems on this topic will also be discussed.



报告题目:The Hermitian-Yang-Mills flow

报告摘要:In this talk, we will introduce our recent works on the Hermitian-Yang-Mills flow on holomorphic vector bundles and its applications. These works are joint with Jiayu Li, Yanci Nie, Changpeng Pan and Chuanjing Zhang.



报告题目:Tangent cone structure of Ricci flow limit

报告摘要:In this talk, we will discuss the tangent cone structure of Ricci flow limit with bounded scalar curvature. The talk is based on Bamler's papers(arXiv:1512.08527 and arXiv:1603.05235).



报告题目:Compactness and structure theory of non-collapsed limits of Ricci flows

报告摘要:We will introduce the recent three preprints of Richard Bamler. First, we will introduce the basic notions, like Wasserstein distance, variance, the Nash entropy and talk about their important properties. Then we will briefly introduce the notion of metric flows, and show that Ricci flow (as a subset of metric flow) have compactness under the so-called F-distance. Finally we will introduce the properties of the limiting spaces, and try to introduce the important ingredients in the progress of establishing this structure theory.