Isospectrality and Commensurability

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.