For more information about this meeting, contact Robert Vaughan.

Title: | Hilbert's Tenth Problem in complementary subrings of number fields |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Kirsten Eisentraeger, Penn State University |

Abstract: |

In this talk I will prove that Hilbert's Tenth Problem is undecidable for subrings of algebraic number fields that are complementary in a very strong
sense. I will show that the non-archimedean primes of a number field $K$ can be partitioned into $t$ disjoint recursive subsets $S_1, \dots, S_t$ (for any $t >1$) such that Hilbert's Tenth Problem is undecidable for the corresponding rings of $S_i$-integers. The only assumption on $K$ is that there is an elliptic curve of rank one defined over $K$. This is joint work with Graham Everest and Alexandra Shlapentokh. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 10 / 14 / 2010 |

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