Divide bounded sets into sets having smaller diameters

主讲人：吴森林 中北大学教授

时间：2022年12月25日15：00

地点：腾讯会议 850 6441 4458

举办单位：数理学院

主讲人介绍：吴森林，中北大学数学学院教授、博士生导师。主要研究方向包括Banach空间理论以及凸和离散几何。正在主持国家自然科学基金面上项目1项；主持完成国家自然科学基金面上项目与青年基金项目各1 项、德国DFG合作交流项目3项、德国DAAD合作交流项目1项、博士后科学基金特别资助项目和博士后科学基金面上项目各1项、其它省部级科研项目3项； 发表学术论文40余篇，其中30余篇被SCI 收录，1篇论文入选ESI高被引 论文。曾获黑龙江省科学技术二等奖1项，受邀出席2019年华人世界数学家大会(ICCM, 北京)并做45分钟报告。

内容介绍：For each positive integer 𝑚 and each real finite dimensional Banach space 𝑋, we set 𝛽􁈺𝑋, 𝑚􁈻 to be the infimum of 𝛿 ∈ 􁈺0,1􁈿 such that each set 𝐴 ⊂ 𝑋 having diameter 1 can be represented as the union of 𝑚 subsets of 𝐴 whose diameters are at most 𝛿 . Elementary properties of 𝛽􁈺𝑋, 𝑚􁈻, including its stability with respect to 𝑋 in the sense of Banach- Mazur metric, are presented. Two methods for estimating 𝛽􁈺𝑋, 𝑚􁈻 as well as their applications are introduced. These results and methods are closely related to the extension of Borsuk's problem in finite dimensional Banach spaces and to C. Zong's computer program for Borsuk's conjecture.