- 06June 6, 2021No events
- 07June 7, 2021No events
- 08June 8, 2021
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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- 09June 9, 2021
CMSA Quantum Matter in Mathematics and Physics: Fracton critical point and Topological phase transition beyond renormalization
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.
- 10June 10, 2021
CMSA Interdisciplinary Science Seminar: The deformation space of geodesic triangulations and Tutte’s embedding
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.
CMSA Quantum Matter in Mathematics and Physics: Minimal nondegenerate extensions and an anomaly indicator
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.
- 11June 11, 2021No events
- 12June 12, 2021No events