New dynamical characterization of countable amenable groups   




报告摘要:Since von Neumann studied the well-known Banach-Tarski paradox in 1929, till now there are many characterizations for amenable groups. In this talk I will report a new characterization of countable amenable groups from the viewpoint of dynamical system. Namely we introduce a new concept called multiorder, and prove that a countable group G is amenable if and only if there exists a multiorder on G. I will also discuss briefly some applications of this new characterization. The talk is based on joint works with Downarowicz, Huczek, Oprocha and Wiecek.