Tiling structure of amenable groups, with applications to symbolic extension and comparison

发布时间：2024-09-09 作者：浏览次数：

Speaker:	张国华	DateTime:	2024年9月12日（周四）上午 9:00-10:00
Brief Introduction to Speaker: 复旦大学教授、博士生导师。主要研究动力系统的复杂性理论和可数离散群作用动力系统的熵理论。在Mem. AMS, J. Reine Angew. Math., Adv. Math., JFA, JDE, ETDS等国际知名刊物上发表论文30余篇。承担了国家自然科学基金优秀青年基金、面上项目等多项科研项目。		Place:	腾讯会议：477-376-598
Abstract:Since the introduction of the concept of amenable groups by von Neumann in 1929 while studying the well-known Banach-Tarski paradox, the structure of amenable groups has remained a bit mysterious. In their seminal work published in 1987, Donald Ornstein and Benjamin Weiss developed the machinery of quasitiling for amenable groups. To further understand the structure of amenable groups, my colleagues and I proved a finitileability theorem, and then solved a question about the tileability of countable amenable groups using finitely many tiles with good invariance properties. This question had remained open for a long time. In this talk, I will present our finitileability theorem, which enhances the Ornstein-Weiss quasitiling machinery for amenable groups. Additionally, if time permits, I will discuss the applications of our finitileability theorem in the symbolic extension theory of amenable group actions and the comparison property of amenable groups. This talk is based on joint work...