For more information about this meeting, contact Robert Vaughan.

Title: | Expander families and variation of Galois representations |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Chris Hall, University of Wyoming |

Abstract: |

Given a pair of curves U,V over the complex numbers, one can associate to a finite unramified map V-->U a finite Cayley-Schreier graph. In this talk we consider families of maps V_i-->U indexed by a parameter i such that the family of associated graphs is an expander family. As we will explain, the expander hypothesis has remarkable geometric implications, e.g. the set of V_i such that the gonality of V_i is less than your favorite positive number N is finite. We will also explain some of the arithmetic implications, e.g. for all but finitely many V_i, there are only many points on V_i defined over some extension of K of degree at most N. As one an application, we can derive results on the variation of Galois representations in a one-parameter family of abelian varieties defined over a number field. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 02 / 07 / 2013 |

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