For more information about this meeting, contact Robert Vaughan.

Title: | Prime factors of dynamical sequences |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Xander Faber, McGill University |

Abstract: |

Euclid's proof that there are infinitely many primes can be recast as a statement about the existence of primitive prime factors of a certain sequence defined by a polynomial dynamical system on the projective line. I will describe a few generalizations of this dynamical statement for arbitrary rational functions. On the arithmetic side, this gives infinitely many new proofs that there are infinitely many primes. On the geometric side, it gives information about the mod p structure of orbits for dynamical systems. The proofs are an amusing mixture of ideas from number theory and complex dynamics. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 10 / 01 / 2009 |

Time: | 11:15am - 12:05pm |