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Sol 3-Manifolds and Hilbert-Blumenthal Surfaces

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Joe Quinn (MoMath)

Abstract: Hilbert modular surfaces were introduced by David Hilbert around 1893, and his student Otto Blumenthal gave the first description of them in his doctoral thesis in 1903. These lie at an interesting juncture of topology and geometry, but many of their geometric properties have remained elusive. We'll see how to form the first geometrically accurate fundamental domain for the cusps of these, whose cross sections canonically represent every commensurability class of the Sol 3-manifolds. Joint with Alberto Verjovsky.