Research output: Contribution to journal › Article › peer-review

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
---|---|

Date | E-pub ahead of print - 3 Mar 2016 |

Date | Published (current) - Jul 2016 |

Issue number | 1 |

Volume | 161 |

Pages (from-to) | 65-85 |

Early online date | 3/03/16 |

Original language | English |

We establish a connection between gaps problems in Diophantine approximation and the frequency spectrum of patches in cut and project sets with special windows. Our theorems provide bounds for the number of distinct frequencies of patches of size r, which depend on the precise cut and project sets being used, and which are almost always less than a power of log r. Furthermore, for a substantial collection of cut and project sets we show that the number of frequencies of patches of size r remains bounded as r tends to infinity. The latter result applies to a collection of cut and project sets of full Hausdorff dimension.

## Career Acceleration Fellowship: Circle rotations and their generalisation in Diophantine approximation

Project: Research project (funded) › Research

## Diophantine approximation, chromatic number, and equivalence classes of separated nets

Project: Research project (funded) › Research

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