报告题目：Universality of Amenable Group Actions

报 告 人：张国华 教授 （复旦大学）

报告时间：2025年12月10日（星期三）9:00- 10:00

报告地点：数学科学学院114      

校内联系人： 侯晓博 副教授   联系方式：84708351-8301

报告摘要：Let (X, G) be a topological dynamical system with positive entropy h, where G is an amenable group. The system (X, G) is called universal if, for any free ergodic G-system (Y, ν, G) with entropy h(ν) < h, there exists an invariant measure µ on X such that the systems (X, µ, G) and (Y, ν, G) are measurably isomorphic. In private communications Benjy Weiss conjectured that each K-shift is universal where K is a finite subset of G containing at least two elements and K-shift is the G-subshift over {0, 1} symbols consisting of the indicator functions of all maximal K-separated sets. In this talk, we shall report our recent result which answers completely the above mentioned problem. Our main result states that a G-subshift with specification is universal if and only if the subshift contains at least one free element, particularly, any K-shift with finite # K > 1 is universal if and only if the subshift contains a free element. This is a joint work with Downarowicz, Weiss and Wiecek.

报告人简介：张国华，2007年7月博士毕业于中国科学技术大学数学系（现为数学科学学院），2013年起任职复旦大学数学科学学院教授。研究方向是拓扑动力系统，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40余篇。