基础数学系学术报告

--- 微分几何讨论班(2024秋季第1讲)

题目: On compactness of sequences of manifolds with nonnegative scalar curvature

报告人: 王常亮 副教授 （同济大学）

时间：2024-9-26  14：15-15：00    

地点：沙河主E404

摘要: Gromov and Sormani conjectured that a sequence of three dimensional Riemannian manifolds with nonnegative scalar curvature and some additional uniform geometric bounds should have a subsequence which converges in some sense to a limit space with generalized notion of nonnegative scalar curvature. In this talk, I will discuss this conjecture, and report our works, joint with Brian Allen, Jiewon Park, Christina Sormani, and Wenchuan Tian, on this problem. In particular, we proved some precompactness results for sequences of warped product three dimensional manifolds with nonnegative scalar curvature, and for sequences of metrics in conformal classes.

报告人简介: 王常亮，同济大学数学科学学院特聘研究员，2016年获加州大学圣芭芭拉分校博士学位，先后在加拿大麦克马斯特大学和德国马普数学所从事博士后研究。研究领域为微分几何与几何分析，主要研究爱因斯坦度量稳定性、非负数量曲率流形收敛性等问题，已在Math. Ann., CAG, JGA, Math. Res. Lett., AGAG等国际著名期刊上发表了十多篇论文。

邀请人：张世金、谢振肖