For more information about this meeting, contact Jason Rute, Stephen Simpson, Jan Reimann.

Title: | Uniform distribution and algorithmic randomness |

Seminar: | Logic Seminar |

Speaker: | Jeremy Avigad, Carnegie Mellon University |

Abstract: |

A seminal theorem due to Weyl states that if (a_n) is any sequence of distinct integers, then, for almost every real number x, the sequence (a_n x) is uniformly distributed modulo one. In particular, for almost every x in the unit interval, the sequence (a_n x) is uniformly distributed modulo one for every *computable* sequence (a_n) of distinct integers. Call such an x *UD random*. Every Schnorr random real is UD random, but there are Kurtz random reals that are not UD random. On the other hand, Weyl's theorem still holds relative to a particular effectively closed null set, so there are UD random reals that are not Kurtz random. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 10 / 21 / 2014 |

Time: | 02:30pm - 03:45pm |