For more information about this meeting, contact Robert Vaughan, Karl Schwede, Mihran Papikian, Ae Ja Yee.

Title: | Portraits of rational functions modulo primes |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Tom Tucker, University of Rochester |

Abstract: |

Let F be a rational function of degree > 1 over a number
field or function field K and let z be a point that is not preperiodic. Ingram and Silverman conjecture that for all but finitely many positive integers (m,n), there is a prime p such that z has exact preperiodic m and exact period n (we call this pair (m,n) the portrait of z modulo p). We present some counterexamples to this conjecture and show that a generalized form of abc implies -- one that is true for function fields -- implies that these are the only counterexamples. One may also ask a similar question for tuples of portraits for several point in a number field or function field. This work is still in progress. The talk represents joint work with several other authors. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 11 / 06 / 2014 |

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