报告名称：On two questions of James

主讲人：彦文娇 教授

邀请人：几何团队

时间：2023年03月24日    16:30

地点：江南娱乐体育官网入口122学术报告厅

主办单位：江南娱乐体育官网入口

报告摘要

There are a number of fascinating and important properties of the Stiefel manifolds Vk(Rn), Vk(Cn) and Vk(Hn), which are defined to be the set of all orthonormal k-frames in Rn, Cn, or Hn with respect to real, complex or quaternionic inner products.

In 1958, I.M.James defined octonionic Stiefel spaces Vk(On)—the space of orthonormal k-frames in On with natural topology and raised two fundamental questions about Vk(On):

(1) Is the projection π:Vk(On) → Vq(On)(q < k) a fiber map ?

(2) Is Vk(On) a manifold ?

We gave partial answers to both of them. This talk is based on joint works with Professor Zizhou Tang and Professor Chao Qian.    

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》等国际著名数学期刊上。