主持人：郑宇
报告人简介：
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, 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, 现为美国罗格斯(Rutgers)大学数学系杰出（Distinguished）教授。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。
报告摘要：
Let X be a compact Gromov-Hausdorff limit space of a collapsing sequence of compact asphercial n-manifolds $M_i$ of Ricci curvature $Ric_{Mi} ≥ ?(n? 1)$ and any point in the Riemannian universal covering space of $M_i$ is a Reifenberg point, or sectional curvature $sec_{M_i} ≥ ?1$, respectively. We conjecture that if the fundamental group of $M_i$ satisfies a certain condition, then X is diffeomorphic, or homeomorphic to an aspherical manifold, respectively. In this talk, we will present a result that if $M_i$ a diffeomorphic or homeomorphic to a nilmanifold, respectively, then X is diffeomorphic or homeomorphic to a nilmanifold, respectively.
