Monday, March 20 at 4:30pm to 5:30pm
Kaprielian Hall (KAP), 245
3620 South Vermont Avenue, Los Angeles, CA 90089
Ian Le, Perimeter Institute
Higher Teichmüller spaces are a component of the character variety for a topological surface S and groups like SL_n(R). These spaces have a parameterization by cluster coordinates, and these cluster coordinates have a natural tropicalization. This leads to the tropicalization of higher Teichmüller space, which can be considered as a generalization of laminations which we call higher laminations. I will show that higher laminations can be realized via actions on affine buildings. This generalizes the association of classical laminations to R-trees. I will emphasize how tropical geometry reflects the piecewise-linear metric geometry of the affine building. I will try to show that higher laminations are concrete and computable objects, and I will draw analogies between the cases of SL_n, n > 2, and the classical case where n=2.