时间：2023年10月11日（星期三）14:00
地点：E4-233
主持人：西湖大学理论科学研究院 傅鑫
主讲人：北京大学 周胜铉
报告主题：The topological stability and unstability of tori with lower Ricci bound
报告摘要：
In this talk, I will introduce a topological stability result given by Bruè-Naber-Semola [BNS23]. They proved that the Gromov-Hausdorff limit of a sequence of Riemannian metrics on torus with bounded diameter and sectional curvature lower bound is a topological torus. Then they pose a question: can we replace the sectional curvature lower bound by Ricci curvature lower bound? In the 3-dimension case, they give an affirmative answer. Then I will describe why the answer of this question should be negative in higher dimension case.
Reference: [BNS23] E. Bruè, A. Naber, D. Semola: Stability of Tori under Lower Sectional Curvature, preprint. https://arxiv.org/abs/2307.03824.
[Z23] S. Zhou: On the Gromov-Hausdorff limits of Tori with Ricci curvature lower bound, preprint. https://arxiv.org/abs/2309.10997.
