Geometry & Topology Seminar: Higher Laminations and Affine Buildings

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

Abstract:
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.

 

 

 

Event Type

Lecture / Talk / Workshop

Campus

University Park Campus

Department

Mathematics

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