|Location:||3 Evans Hall|
The topology of arithmetic hyperbolic 3-manifold is closely tied to number theory. For example, starting from an elliptic curve over Q(i), we can (conjecturally) find a "corresponding" homology class in H_2(M) where M is a finite cover of the Bianchi manifold associated to SL_2(Z[i]).
After some motivation, I will suggest that the topological complexity (e.g. Thurston norm) of this homology class should be related to the arithmetic complexity (the height) of the elliptic curve. At the end I will briefly discuss the general situation (i.e., for general arithmetic groups).
There will be a related talk by the speaker in 740 Evans at 2:10pm to explain some background on arithmetic groups. In particular, he will explain why number theorists are keenly interested in these groups.No Notes/Supplements Uploaded No Video Files Uploaded