Groups and Dynamics Seminar

Date: November 3, 2021

Time: 3:00PM - 4:00PM

Location: online

Speaker: Yuqing Frank Lin, Texas A&M

Title: On Invariant Random Orders

Abstract: We introduce a probabilistic analog of left-invariant total orders on countable groups called (left) invariant random orders (IROs). IROs have been applied in recent years to obtain results in entropy theory by providing a notion of a "past". We discuss several questions on IROs in analogy to (deterministic) left-invariant orders. For example IROs can be seen to be more flexible than (deterministic) left-invariant orders- IROs always exist for any countable group and partial orders can be extended to IROs for any amenable group. Nevertheless, we show an example of a partial order that cannot be extended to an IRO. Joint work with Yair Glasner and Tom Meyerovitch.