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Groups And Dynamics
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Jon Chaika, 10.146: A prime system with many and big self-joinings
Friday, September 13, 2019, 02:00pm - 03:00pm
Let (X,mu,T) be a measure preserving system. A factor is a system(Y,nu,S) so that there exists F with SF=FT and so that F pushesmu forward to nu. A measurable dynamical system is prime if ithas no non-trivial factors. A classical way to prove a systemis prime is to show it has few self-joinings, that is, few Tx T invariant measures that on X x X that project to mu. We showthat there exists a prime transformation that has many self-joiningswhich are also large. In particular, its ergodic self-joiningsare dense in its self- joinings and it has a self-joining thatis not a distal extension of itself. As a consequence we showthat being quasi-distal is a meager property in the set of measurepreserving transformations, which answers a question of Danilenko.This is joint work with Bryna Kra.
Location: 10.146

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