A Banach space is said to have the ball coveringproperty if its unit sphere can be covered by countably many open balls off theorigin. The ball covering property is a property that has close relationshipswith the topological properties and geometric properties of Banach spaces. Inthis talk, we will give a review of the historical literature and present somerecent advances on this topic. Open problems will be proposed, and approacheswill be discussed.

郑本拓，获美国Texas A&MUniversity数学博士学位，是美国孟菲斯大学数学系教授，主要研究方向为Banach空间理论及其应用，郑本拓教授在Banach空间理论领域获得了诸多杰出的成果。例如:解决了著名的具有无条件基Banach空间的子空间的刻画问题，回答了泛函分析国际顶级专家H.Rosenthal提出的一个三十多年的公开问题；运用Banach空间理论，对调和分析领域关于Lp空间函数平移的公开问题给出否定回答；完全证明弱有界逼近性质和强逼近性质对于任意Banach空间的等价性，解决了逼近性质资深专家Oia的猜想。郑本拓教授国际著名数学期刊Duke Math Journal，Transactions of AMS以及Journal of Functional Analysis等发表论文多篇。