# abstract

LIE GROUPS, REPRESENTATIONS AND DISCRETE MATH | |

Topic: | Isospectrality and Commensurability |

Speaker: | Alan Reid |

Affiliation: | University of Texas, Austin |

Date: | Tuesday, April 4 |

Time/Room: | 2:00pm - 3:15pm/S-101 |

In previous work we showed that arithmetic hyperbolic 2-manifolds that are isospectral are commensurable. In this talk we discuss the proof of the generalization to dimension 3. We had previously shown that if arithmetic hyperbolic 3-manifolds are complex iso-length spectral they are commensurable. What we will actually prove here is that arithmetic hyperbolic 3-manifolds that are iso-length spectral are commensurable. The proof has some surprising consequences for the galois theory of fields with one complex place.