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Junior Geometry
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Josh Vekhter, RLM 12.166: Building Better Bunny Baskets
Tuesday, December 03, 2019, 03:45pm - 04:45pm
Given the task of weaving a basket in the shape of a bunny, weturn to the tomes of differential geometry for guidance. Wefind that objects made out of thin ribbons implicitly describe(approximately) geodesic (almost) foliations --- i.e. decompositionsof implicit 2-manifolds into leaves which are everywhere closeto geodesics. Flipping the problem on it's head, we put togethera computational pipeline for recovering such foliations on arbitrary2-manifolds in order to enable computer assisted weaving of arbitraryforms. The key ingredient is the observation that vector fieldswhich are unit and integrable are geodesic. We develop a computationalmethod to find such fields, recovering minimizers of a PDE whichalso appears in the study of liquid crystals (sometimes goingby the moniker of the aviles-giga functional). Time permitting,we might even end up weaving a torus.
Location: RLM 12.166

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