走向现代数学学术报告 - 金磊副教授（No. 641）

报告题目：Sofic approximation sequences and sofic mean dimension

报 告 人：金磊 副教授（中山大学）

报告时间：2023年6月23日（星期五） 10:30

报告地点：工西417

报告摘要：In this talk we will prove that sofic mean dimension of any amenable group action does not depend on the choice of sofic approximation sequences. Previously, this result was known only if the acting group is an infinite amenable group; however, in the case of a finite group action, this knowledge was restricted to finite-dimensional compact metrizable spaces only. We will also show that sofic mean dimension of any full shift depends purely on its alphabet. Previously, this was shown only when the alphabet is a finite-dimensional compact metrizable space. I will start with the background and basic notions, and explain the differences between our method and the classical technique in relation to the estimates for mean dimension. The key point of our results is that they apply to all compact metrizable spaces without any restriction (in particular, any of the alphabets and spaces concerned in our results is not required to be finite-dimensional). This is a joint work with Yixiao Qiao.

报告人简介

金磊，中山大学数学学院副教授，主要研究方向为拓扑动力系统，尤其是平均维数理论，相关学术研究论文发表于 Math. Ann., Fund. Math., Proc. Amer. Math. Soc., Nonlinearity, ETDS, JDE 等期刊。