报告题目： Dimension, comparison, and almost finiteness 报 告 人： Prof. David Kerr 报告人所在单位： 报告日期： 2017-06-14 星期三 报告时间： 15:00-16:00 报告地点： Texas A&M University 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 todynamical 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. 本年度学院报告总序号： 138