{"date":"2022-05-23","starts":{"hour":11,"minute":0,"second":0,"second_of_day":39600},"ends":{"hour":12,"minute":0,"second":0,"second_of_day":43200},"room":"Building 32, room 114","speaker":"Zhuang Niu","from":"University of Wyoming","title":"Structure of crossed product $$C^*$$-algebras","abstract":"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.\r\n\r\n\r\n","speaker_web":null,"announcement":null,"descfiles_signed_ids":"[]","online":false,"slug":"2022-05-23","shift":{"beginning":{"hour":11,"minute":0,"second":0,"second_of_day":39600},"ending":{"hour":12,"minute":0,"second":0,"second_of_day":43200},"exclude_end":false,"range":"[39600,43200]"},"announcement_i18n":{"en":"","he":""},"duration":"[2022-05-23 08:00:00 UTC,2022-05-23 09:00:00 UTC]","id":892,"created_at":"2022-05-21T20:00:36.342+03:00","updated_at":"2022-05-22T23:20:28.716+03:00","admin_users":[],"summary":"Zhuang Niu: Structure of crossed product $$C^*$$-algebras","full_speaker_text":"Zhuang Niu (*University of Wyoming*)","unusual":"place","unusual_place":true,"unusual_time":false,"unusual_day":false}