Date
Wed, 25 Jan 2012
Time
16:00 - 17:00
Location
SR2
Speaker
Andrew Sale

The lamplighter groups, solvable Baumslag-Solitar groups and lattices in SOL all share a nice kind of geometry. We'll see how the Cayley graph of a lamplighter group is a Diestel-Leader graph, that is a horocyclic product of two trees. The geometry of the solvable Baumslag-Solitar groups has been studied by Farb and Mosher and they showed that these groups are quasi-isometric to spaces which are essentially the horocyclic product of a tree and the hyperbolic plane. Finally, lattices in the Lie groups SOL can be seen to act on the horocyclic product of two hyperbolic planes. We use these spaces to measure the length of short conjugators in each type of group.

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