Robin D. Tucker-Drob

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We show that for any infinite countable group G and for any free Borel action G y X there exists an equivariant class-bijective Borel map from X to the free part Free(2G) of the 2-shift G y 2G. This implies that any Borel structurability which holds for the equivalence relation generated by Gy Free(2G) must hold a fortiori for all equivalence relations(More)
This note answers a question of Kechris: if H < G is a normal subgroup of a countable group G, H has property MD and G/H is amenable and residually finite then G also has property MD. Under the same hypothesis we prove that for any action a of G, if b is a free action of G/H, and bG is the induced action of G then CInd G H(a|H)×bG weakly contains a.(More)
A measure preserving action of a countably in nite group Γ is called totally ergodic if every in nite subgroup of Γ acts ergodically. For example, all mixing and mildly mixing actions are totally ergodic. This note shows that if an action of Γ is totally ergodic then there exists a nite normal subgroup N of Γ such that the stabilizer of almost every point(More)
Abért and Weiss have shown that the Bernoulli shift s0 of a countably infinite group 0 is weakly contained in any free measure preserving action a of 0. Proving a conjecture of Ioana, we establish a strong version of this result by showing that s0 × a is weakly equivalent to a. Using random Bernoulli shifts introduced by Abért, Glasner, and Virag, we(More)
The last two decades have seen the emergence of a theory of set theoretic complexity of classification problems in mathematics. In these lectures we will discuss recent developments concerning the application of this theory to classification problems in ergodic theory. The first lecture will be devoted to a general introduction to this area. The next two(More)