报告名称：Topology and curvature of isoparametric families

报告专家：彦文娇

专家所在单位： 北京师范大学

报告时间：2021年4月18日14:00-14:50

报告地点： 腾讯会议274 617 925

专家简介：彦文娇，国家优秀青年基金获得者，现任北京师范大学数学学院教授，博士生导师。主要研究领域是微分几何，特别是等参超曲面、等参函数及其相关应用，代表性成果包括完全解决了等参情形的丘成桐第一特征值猜想，给出了Besse问题的一系列单连通例子等。主要研究成果均发表在J. Diff. Geom.,Advances in Math.,J. Funct. Anal.,Comm. Anal. Geom., Sci. China Math.,Math. Z.,IMRN等国际高水平数学期刊上。

报告摘要：In this talk, we will introduce topology of the isoparametric families in spheres, including the homotopy, homeomorphism, or diffeomorphism types, parallelizability, as well as the Lusternik-Schnirelmann category, and their curvatures, more precisely, we determine when they have non-negative sectional curvatures or positive Ricci curvatures with the induced metric.

Besides, we construct a transnormal system with transnormal hypersurfaces diffeomorphic to the Gromoll-Meyer sphere Σ^7, each hypersurface with the induced metric has positive Ricci curvature and quasi-positive sectional curvature simultaneously. This talk is based on joint works with Prof. Zizhou Tang and Prof. Chao Qian.

邀请人： 毛井