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Cross-ratio dynamics on ideal polygons


Speaker: Sergei Tabachnikov, Pennsylvania State University
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Location: 3106 MSB
Start time: Tue, Nov 19 2019, 1:30PM

Define a relation between labeled ideal polygons in the hyperbolic 3-space by requiring that the complex distances (a combination of the distance and the angle) between their respective sides equal a constant; the constant is a parameter of the relation. This gives a 1-parameter family of maps on the moduli space of ideal polygons in the hyperbolic space (or, in its real version, in the hyperbolic plane). I shall discuss complete integrability of this family of maps and related topics, including -time permitting - a continuous version of this relation that is intimately related with the Korteweg-de Vries equation.