勷勤数学•专家报告

题      目：Universality of Actions by Amenable Groups

报  告  人：张国华 教授  (邀请人：谭枫)

                                              复旦大学

时      间：1月16日  10：30-11：30

地     点：数科院西楼二楼会议室

报告人简介:

           张国华，复旦大学数学科学学院教授、博士生导师，国家优青，本硕博均毕业于中国科学技术大学数学系（现为数学科学学院），博士论文入选全国百篇优秀博士论文，曾相继获得香港求是科技基金会研究生奖、中国科学院院长特别奖、瑞士科技部设立的 2007 年应用数学欧拉奖等。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。曾在Memoirs Amer. Math. Soc., J. Reine Angew. Math., Adv. Math., Ergod. Th. Dynam. Systems, J. Mod. Dyn., J. Funct. Anal., J. Differential Equations等国际权威刊物上发表论文30余篇。

摘      要：

       Let (X, G) be TDS with positive topological 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 this talk, we shall report our recent result that a G-subshift with specification is universal if and only if the space contains at least one free element, particularly, any K-shift (consisting of the indicator functions of all maximal K-separated sets) with K finite nonempty is universal if and only if the space contains a free element. This is a joint work with Downarowicz, Weiss and Wiecek.

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