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Local testability in group theory II

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NPCW04 - Approximation, deformation, quasification

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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