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June 10
  • 10
    June 10, 2021

    CMSA Interdisciplinary Science Seminar: The deformation space of geodesic triangulations and Tutte’s embedding

    9:00 AM-10:00 AM
    June 10, 2021

    In 1984, Bloch, Connelly, and Henderson proved that the space of geodesic triangulations of a convex polygon is contractible. It was found that Tutte’s embedding theorem could give a very simple proof to Bloch-Connelly-Henderson’s theorem, and provides an elegant algorithm for image morphing on convex polygons. We recently generalize Tutte’s embedding theorem, and prove that the deformation space of geodesic triangulations of a closed Riemannian surface of negative curvature is contractible. This confirms a conjecture by Connelly, Henderson, Ho, Starbird in 1983, and also indicates a method for image morphing on closed surfaces.

    Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09

    (Password: 419419)

    CMSA Quantum Matter in Mathematics and Physics: Minimal nondegenerate extensions and an anomaly indicator

    10:30 AM-12:00 PM
    June 10, 2021

    Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.

    Zoom: https://harvard.zoom.us/j/977347126