Title: For a countable discrete group Γ to be relative to a subgroup Λ ≤ Γ. Then prove all the equivalences
Speaker: Peter Huston (The Ohio State University)
Abstract: Topologically ordered phases of matter are a subject which can be approached from a number of perspectives, including the perspective of lattice models, where topological order arises from systems of local operators on a Hilbert space. I will introduce lattice models of 2+1D topological order and 1+1D topological boundaries between them, and outline the relationship between these models and tensor categories which classify their topological order. A pair of parallel topological boundaries can decompose as a direct sum, a phenomenon which can be seen concretely in lattice models. In recent join work with Fiona Burnell, Corey Jones, and Dave Penneys, we have used the graphical calculus of 3-categories of enriched fusion categories to understand how this decomposition can be computed algebraically.