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Logic Seminar

Wednesday, April 29, 2020
12:00pm to 1:00pm
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Online Event
Tiling properties and pointwise ergodic theorems
Jenna Zomback, Department of Mathematics, University of Illinois at Urbana-Champaign,

A pointwise ergodic theorem for the action of a countable group Gamma on a probability space equates ergodicity of the action to its a.e. pointwise combinatorics. One result (joint work with Jon Boretsky) we will discuss is a short, combinatorial proof of the pointwise ergodic theorem for free, probability measure preserving (pmp) actions of amenable groups along Tempelman Følner sequences, which is a slightly less general version of Lindenstrauss's celebrated theorem for tempered Følner sequences. In fact, we prove that such actions have a certain tiling property, which implies the pointwise ergodic theorem. Another result we will discuss is a similar tiling property in the quasi-pmp setting for the natural boundary actions of the free group on n generators (n < infty), which implies the corresponding pointwise ergodic theorem.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].