Pappus's theorem, the modular group, and patterns of geodesics

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• Richard Schwartz (Brown University)
• Friday 11 July 2025, 09:15-10:15
• Seminar Room 1, Newton Institute.

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NPCW06 - Non-positive curvature and applications

This talk reports on a mixture of old and new work concerning the construction of representations of the modular group into Isom(X) using Pappus’s Theorem. Here  X = SL_3®/SO(3) .   One new thing is the interpretation of the Pappus modular groups as symmetry groups of patterns of geodesics in X which have the same asymptotic properties as the edges of the Farey triangulation of the hyperbolic plane.    I will explain at least briefly how this point of view leads to a complete characterization of the Barbot component of discrete faithful representations of the modular group into Isom(X).

This talk is part of the Isaac Newton Institute Seminar Series series.

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