### Zhuang Niu (University of Wyoming)

Monday, May 23, 2022, 11:00 – 12:00, Building 32, room 114

Consider a dynamical system, and let us study the structure of the corresponding crossed product $C^*$-algebra, in particular on the classifiability, comparison, and stable rank. More precisely, let us introduce a uniform Rokhlin property and a relative comparison property (these two properties hold for all free and minimal $Z^d$ actions). With these two properties, the crossed product $C^*$-algebra is shown to always have stable rank one, to satisfy the Toms-Winter conjecture, and that the comparison radius is dominated by half of the mean dimension of the dynamical system.