| Time: | 12:30 - 13:30 |
| Room: |
Wean Hall 7201
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| Speaker: |
Clinton Conley Department of Mathematical Sciences CMU |
| Title: |
Borel marker sets and hyperfiniteness
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| Abstract: | A classical tool in ergodic theory is the Rokhlin lemma, which more or less states that any ergodic measure-preserving automorphism of a standard probability space is the uniform limit of periodic automorphisms. At its combinatorial core, the lemma's proof relies on the ability to find measurable sets which intersect every orbit in a reasonably spaced out fashion. We discuss analogs of this in the purely Borel context, and use such marker sets to prove the Slaman-Steel / Sullivan-Weiss-Wright result that every Borel action of the integers on a standard Borel space generates a hyperfinite orbit equivalence relation. Time permitting, we discuss the (still open) problem of extending this to actions of arbitrary countable amenable groups, in preparation for Su Gao's Appalachian Set Theory workshop this October. |