走向现代数学学术报告 - 梁先娟（No. 965)

报告题目：Subsets relative to filterduals on a discrete semigroup that force recurrence

报 告 人：梁先娟 讲师（云南师范大学）

邀 请 人：李健 教授

报告时间：2026年9月21日 16点

报告地点：东海岸校区D209

报告摘要： Let $S$ be an infinite discrete semigroup.

A filterdual F on S is a Furstenberg family (the collection of subsets of S which is hereditary upwards) whose dual family is a filter. In this paper we propose an alternative way to define notions of subsets of a discrete semigroup relative to a filterdual F, including F-thick, F-syndetic, piecewise F-syndetic, thickly F-syndetic, F-central, F-quasi central sets. We characterize those kinds relative subsets by the properties that force recurrence in topological dynamics.

个人简介： 梁先娟，女，云南师范大学数学学院讲师，任职于基础数学系（部）。主要研究领域为拓扑动力系统与遍历论，已在Proceedings of the American Mathematical Society、Fundamenta Mathematicae等期刊发表多篇文章。主讲本科生课程有《数学分析》、《高等数学》。