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Junior Geometry
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Hunter Vallejos, Zoom: Randomly sampling half-translation surfaces
Tuesday, March 30, 2021, 03:45pm - 04:45pm
We will discuss a recent theorem of Francisco Arana-Herrera which states that horoball segment measures on the bundle of unit-length measured geodesic laminations over the moduli space of hyperbolic surfaces equidistribute with respect to Mirzakhani measure. After a brief overview of the proof, we will discuss an application of this theorem, which gives a concrete recipe to randomly sample hyperbolic surfaces. Once we have a random hyperbolic surface, we can use train tracks to randomly sample a quadratic differential using the Thurston homeomorphism, thus giving us a random half-translation surface.
Location: Zoom

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