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Tilings of amenable groups and a problem of codeability Downarowicz, Tomasz


We improve Ornstein-Weiss' quasitiling of a countable amenable group to a "perfect" tiling. The price is that the number of shapes increases drastically, nonetheless we manage to keep the entropy equal to zero. It remains a challenge to encode the system of tilings in a 0-1 subshift. So far we can do that only under the additional Tempelman's condition. Joint work with Dawid Huczek and Guohua Zhang. Last part with Maxence Phalempin.

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