BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Konstantin Slutsky (Iowa State University) DTSTART:20230302T190000Z DTEND:20230302T200000Z DTSTAMP:20260423T052839Z UID:OLS/114 DESCRIPTION:Title: Pa rtial actions and orbit equivalence relations\nby Konstantin Slutsky ( Iowa State University) as part of Online logic seminar\n\n\nAbstract\nIn t his talk\, we will discuss the framework of partial actions\nfor construct ing orbit equivalent actions of Polish groups. While\nrelated ideas have b een employed in ergodic theory and Borel\ndynamics for many years\, the pa rticular viewpoint of partial\nactions simplifies construction of orbit eq uivalent actions\nof distinct groups. \n\nAs an application\, we will pre sent a Borel version of Katok's\nrepresentation theorem for multidimension al Borel\nflows. One-dimensional flows are closely connected to actions\no f $\\mathbb{Z}$ via the so-called "flow under a function"\nconstruction. This appealing geometric picture does not\ngeneralize to higher dimensions . Within the ergodic theoretical\nframework\, Katok introduced the concep t of a special flow as a\nway to connect multidimensional $\\mathbb{R}^d$ and $\\mathbb{Z}^d$\nactions. We will show that similar connections conti nue to hold\nin Borel dynamics.\n\nAnother illustration of the partial act ions techniques that we\nintend to touch is the following result: a Borel equivalence\nrelation generated by a free R-flow can also be generated by a\nfree action of any non-discrete and non-compact Polish\ngroup. This is in contrast with the situation for discrete\ngroups\, where amenability di stinguishes groups that can and\ncannot generate free finite measure-prese rving hyperfinite actions.\n LOCATION:https://researchseminars.org/talk/OLS/114/ END:VEVENT END:VCALENDAR