Speaker: Theo Johnson-Freyd (Dalhousie/Perimeter Institute)
Title: The classification of topological orders
Abstract: The Landau Paradigm classifies phases of matter by how "ordered" they are, i.e. by their symmetry groups (and symmetry breaking). The difference between liquids and solids fits into this paradigm, as does the Higgs mechanism that gives particles masses in high-energy physics. However, starting around the turn of the (21st) century, it has become clear that there are patterns of "order" or "symmetry" in quantum matter systems which cannot be described by groups. In particular, there are topological phases of matter, characterized by having no local observables whatsoever, which Landau would have thought were completely trivial but which in fact have subtle long-range topological order. To describe these topological orders requires the mathematics of fusion higher categories. In this talk, I will describe the classification of these topological orders in various dimensions and the extent to which the Landau Paradigm does or does not hold.
URL associated with Seminar
https://web.math.osu.edu/colloquium/
