报告题目：Partition bounded sets into sets having smaller diameters
报 告 人：吴森林 (中北大学教授)
报告时间：2022年5月13日(星期五)上午10:00-11:00
报告形式：腾讯会议ID：885-798-216
内容简介：For each positive integer and each real finite dimensional Banach space, we set to be the infimum of such that eachset having diameter can be represented as the union of subsets of whose diameters are at most . Elementary properties of, including its stability with respect to in the sense of Banach-Mazur metric, are presented. Two methods for estimating are introduced. The first one estimates using the knowledge of, where is a Banach space sufficiently close to . Thesecond estimation uses the information about , the infimum of such that is the union of subsets havingdiameters not greater than times the diameter of , for certainclasses of convex bodies in . In particular, we show that holds for each by applying the first method, and we proved that whenever is a three-dimensional Banach space satisfying , where is the unit ball of , by applying the second method. 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.
报告人简介：吴森林，中北大学理学院教授、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篇论文曾入选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。
（撰稿人：张霞；审稿人：郭永峰）
数学科学学院
2022年5月10日