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  • 天元讲堂(6.15):Dimension, comparison, and almost finiteness
  • 浏览量:239 发布人:佚名 发布时间:2017-06-15 15:55:32
  • 报告题目:Dimension, comparison, and almost finiteness

    报告人:David Kerr , Professor , Texas A&M University

    报告时间:2017年6月15日下午16:30

    报告地点:数学楼306

    报告摘要:I will explain how one can develop a dynamical version of some of the theory surrounding the Toms-Winter conjecture for simple separable nuclear C*-algebras. In particular, I will introduce a notion of almost finiteness for group actions on compact spaces as an analogue of both hyperfiniteness in the measure-preserving setting and of $\mathcal{Z}$-stability in the C*-algebra setting. This generalizes Matui's concept of the same name from the zero-dimensional context and is related to dynamical comparison in the same way that $\mathcal{Z}$-stability is related to strict comparison in the Toms-Winter context. For free minimal actions of countably infinite groups on compact metrizable spaces the property of almost
    finiteness implies that the crossed product is $\mathcal{Z}$-stable, which leads
    to new examples of classifiable crossed products.

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