Friday 16 Nov 2012AG Dynamics Seminar: Double lattice PETs, hyperbolic geometry, and renormalization

Richard Schwartz - Brown University

Poldhu room, Kay Building 14:00-15:00

A polytope exchange transformation (PET) is a piecewise isometric map of a polytope which is based on a partition of the polytope into smaller polytopes in two different ways. I will explain a general way to construction PETs based on pairs of Euclidean lattices and their fundamental domains. The simplest example of the construction yields a 1-parameter family of polygon exchange transformations which turns out to have the (2,4,infty) hyperbolic reflection triangle group acting on the parameter space as the renormalization symmetry group. I'll concentrate on simple down-to-earth corollaries and will illustrate the main results with computer pictures and demos.

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