|LIE GROUPS, REPRESENTATIONS AND DISCRETE MATH|
|Topic:||Isospectrality and Commensurability|
|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.