黄色仓库

报告时间：2026年9月24日（周四）上午 09:00-09:55

报告地点：黄色仓库 天赐庄校区纯水楼301

报告人：张国华 教授，复旦大学

报告摘要：

Let $G$ be a countably infinite group and let $K\subset G$ be finite, with $e\in K$ and $|K|>1$. The $K$-shift $\Omega_K\subset\{0,1\}^G$ consists of the indicator functions of all maximal $K$-separated subsets of $G$. Every $K$-shift has specification, but it need not contain a free point. For arbitrary $G$, we identify a finite normal subgroup $N_K$, called the isotropy core, whose triviality is equivalent to the existence of a free point, topological freeness, faithfulness, and the existence of a free minimal subshift. When $G$ is amenable, we show that a $G$-subshift with specification is universal precisely when it contains a free point. Thus, $\Omega_K$ is universal exactly when $N_K$ is trivial, while the induced $G/N_K$-action is always universal. If $G/N_K$ is torsion-free and residually finite, the entropies of minimal subshifts with stabilizer $N_K$ are dense below $h_{top}(\Omega_K)$. The talk is based on joint works with Tomasz Downarowicz, Benjamin Weiss, Mateusz Więcek, and Hui Xu.

报告人简介：

张国华，复旦大学黄色仓库 教授、博士生导师。研究方向是拓扑动力系统与遍历论，主要研究动力系统的复杂性理论和可数离散群作用的熵理论。在Memoirs Amer. Math. Soc., J. Reine Angew. Math., Adv. Math., Ergod. Th. Dynam. Systems, J. Mod. Dyn., J. Funct. Anal., J. Differential Equations等国际知名刊物上发表论文近40篇。

邀请人：杨大伟