一、报告题目：Solution to the Weiss’ Conjecture of Universal Amenable Group Actions

二、报告人：张国华教授

三、时   间：2025年6月19日（周四）上午10:30-11:30

四、地   点：闻理园A4-218

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. 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 Weiss’ Conjecture. Our main result states that, in general the conjecture does not hold, however, 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近40篇。曾主持多项基金委面上项目及国家优青项目，担任基金委重点项目的骨干成员，曾入选上海市青年拔尖人才，荣获全国百篇优博论文、中科院院长特别奖、瑞士科技部应用数学欧拉奖等。现在正担任科技部国家重点研发计划重点专项“数学和应用研究”的课题负责人。

欢迎广大师生参加！联系人：李先义