报告人：戎小春（美国罗格斯大学）

时 间：2023年7月19日9:30

地 点：厦门大学海韵园实验楼105报告厅

内容摘要:

A complete Riemannian n-manifold M is called epsilon-collapsed, if every unit ball in M has volume less than epsilon (while often a bound on `curvature' must be imposed to prevent a rescaling of metric). In 1978, Gromov classified `almost flat manifolds' (or the `maximally collapsed manifolds' with sectional curvature bounded in absolute value by one and small diameter) ; a bounded normal covering space of M is diffeomorphic to the quotient of a simply connected nilpotent Lie group modulo a manifold up to a co-compact lattice. This result has been a corner stone in the collapsing theory of Cheeger-Fukaya-Gromov in 90's that there is a nilpotent structure on any epsilon-collapsed manifold with bounded sectional curvature, and this theory has found important applications in Metric Riemannian geometry.

We will survey some recent development in generalizing the collapsing theory to epsilon-collapsed manifolds of Ricci curvature bounded below and the (incomplete) universal cover of every unit ball in M is not collapsed. The study of this class of collapsed manifolds is partially fueled with many constructions of collapsed Calabi-Yau metrics using certain underlying singular nilpotent fibrations.

个人简介：

戎小春是国际知名的度量黎曼几何专家, 教育部长江学者特聘教授，现为美国罗格斯(Rutgers)大学数学系杰出（Distinguished）教授。曾获美国斯隆研究奖（Sloan Research Fellowships），美国数学会会士, 应邀在2002年国际数学家大会做45分钟报告。戎小春教授于1978-1984年在首都师范大学获本科和硕士学位, 1990年在纽约州立大学石溪分校获博士学位，毕业后曾在美国哥伦比亚大学和芝加哥大学任教。戎小春教授主要从事微分几何和度量黎曼几何的研究，在黎曼几何中的收敛和塌陷理论及其应用、正曲率流形几何和拓扑，Alexandrov几何等方面作出了若干基础性的贡献，已在Adv. Math., Amer. J. Math.，Ann. of Math，Duke Math.，GAFA.，Invent. Math.，J. Diff. Geom等国际知名期刊上发表论文50余篇。

联系人：宋翀