报告时间：2025.4.30上午10:00-12:00

报告地点：北区4号教学楼208报告厅

报告题目：Universal covering system and Borsuk's problem in finite dimensional Banach spaces

报告摘要：For each $n$-dimensional real Banach space $X$ and each positive integer $m$, let $\beta(X,m)$ be the infimum of $\delta\in (0, 1]$ such that each set $A\subseteq X$ having diameter $1$ can be represented as the union of $m$ subsets of $A$, whose diameters are not greater than $\delta$. It is useful to provide good estimations of $\beta(X,m)$ for certain choices of $X$ and $m$ for attacking the extension of the classical Borsuk's problem in finite dimensional Banach spaces. A general framework for estimating $\beta(X,m)$ via constructing and refining universal covering systems is presented. As an example a universal covering system is constructed in $\ell^3_1$ and it is shown that $\beta(\ell^3_1,8)\leq 11/12$ by a feasible partitioning of members in this universal covering system.

报告人简介：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；发表被SCI收录的学术论文48余篇，1篇论文曾入选ESI高被引论文（被引用129次）。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。