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Number Theory Seminar: Cycle complexity on arithmetic manifolds October 01, 2014 (04:10 PM PDT - 05:00 PM PDT)
Parent Program: --
Location: 3 Evans Hall
Speaker(s) Akshay Venkatesh (Institute for Advanced Study)
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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.

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