Wednesday, April 5 2017 - Thursday, April 6 2017

11:30 - 13:00

11:30 - 13:00

* Venue | Media Centre |

* Speaker | J-M. Deshouillers |

* Title | Cobham’s theorem |

Affiliation | University of Bordeaux |

Abstract | These three lectures present a proof of Cobham’s theorem stated below. They represent the last part of the lectures I gave at IMSc on Automatic sequences. However, this set of lectures is self-contained: no \emph{a priori} knowledge of automatic sequences is required. Cobham’s theorem states that if an infinite set $X$ of integers is both $k$ and $\ell$ automatic, where $\log k$ and $\log \ell$ are $\mathbb{Q}$-linearly independent, then $X$ is ultimately periodic. In lecture 1, we recall definitions and basic facts about automatic sequences and we present a result on Diophantine approximation. In lecture 2, we show that a sequence satisfying the hypothesis of Cobham’s theorem is syndetic, i.e. the difference between its consecutive terms is bounded. In lecture 3, we end the proof of Cobham’s theorem. |

* Announcement? | Public |

* Refreshments? | Before the event |

* Honorarium? | None |

Special Arrangements? | Videography |

* Host name and email |

Done