Calendar

Title: The two-dimensional Ising model revisited

Abstract: I will describe joint work with Constantin Teleman, in which we cast topological eyes on a well-studied system in condensed matter physics.  In particular, we use the symmetry in a strong form and apply the technology of extended topological field theory.  We obtain a proof of duality, construct a new dual theory for models based on a nonabelian group, and make dynamical predictions.  The lecture will not assume any physics background.

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The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.

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

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)

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