报告题目 (Title)：Borsuk’s Partition Problem, Hadwiger’s Covering Conjecutre, and the Boltyanski-Gohberg Conjecture

中文标题：Borsuk 的分区问题、Hadwiger 的覆盖猜想 和 Boltyanski-Gohberg 猜想

报告人 (Speaker)：宗传明（天津大学）

报告时间 (Time)：2023年12月15日(周五) 10:00

报告地点 (Place)：校本部GJ303

邀请人(Inviter)：席东盟、李晋、张德凯

主办部门：理学院数学系

报告摘要：In 1933, K. Borsuk proposed the following problem: Can every bounded set in the n-dimensional Euclidean space be divided into n + 1 subsets of smaller diameters? In 1957, H. Hadwiger made the following conjecture: Every n-dimensional convex body K can be covered by 2 n translates of its interior int(K). In 1965, V. G. Boltyanski and I. T.Gohberg made the following conjecture: Every bounded set in an n-dimensional normed space can be divided into 2 n subsets of smaller diameters. These problems are closely related. Up to now, all of them are far away from being completely solved. In this talk, we will introduce a computer approach to these problems. In particular, we will show an asymptotic solution to the Boltyanski-Gohberg conjecture.