北航数学论坛学术报告

--微分几何讨论班（2021年秋第16讲）

Min-max theory and multiplicity

周鑫

（美国康奈尔大学）

报告时间：9：30-10：30，2022-1-18（星期二）

腾讯会议号： 545-920-009

摘要： In the past decade, we have seen many significant advancements in the min-max theory of minimal hypersurfaces, including the solution of Yau's conjecture and the establishment of a Morse theory for the area functional. As the major challenge of these works, the min-max hypersurfaces are counted with integer multiplicities. In this talk, we will first present the proof of the Multiplicity One Conjecture, which asserts that the multiplicity is always one for generic metrics. In the second part, we will introduce the construction of a set of non-generic metrics in which some min-max minimal hypersurface must have higher multiplicities. The second part is a joint work with Zhichao Wang (UBC).

报告人简介：周鑫，2013年在美国斯坦福大学获得博士学位，现任美国康奈尔大学副教授。主要研究方向是极小曲面理论以及相关问题，解决了极小极大理论中单一重数猜想等著名问题，在Ann. Math., Invent. Math., JDG等顶尖数学期刊上发表多篇论文，并受邀在2022年国际数学家大会上做45分钟报告。

邀请人：沈良明