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Local testability in group theory II

Presented by: 
Oren Becker
Tuesday 9th May 2017 - 10:00 to 11:00
INI Seminar Room 1
This talk is a continuation of Alex Lubotzky's talk with a similar title (but an effort will be made to keep it independent).
We will describe a combinatorial/geometric method to prove testability (or non-testability) in various cases. 
For certain amenable groups, we present a method of "tiling" every Schreier graph by finite Schreier graphs. This is an extension of the work of Weiss on monotileable groups. We then use the tilings to prove testability for those groups by a method which has its origins in the work of Ornstein-Weiss on amenable groups. This enables us to answer some questions posed in a paper by Arzhantseva and Paunescu and extend some of their results. It also suggests many more questions for further research.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons