Yasuyuki Kawahigashi (University of Tokyo/RIKEN): Tensor networks, fusion categories and operator algebras

Passcode: 657361

Speaker: Yasuyuki Kawahigashi 

Title: Tensor networks, fusion categories and operator algebras

Abstract: Certain 4-tensors have been used to study two-dimensional topological order, and we identified them with bi-unitary connections in subfactor theory of Jones before.  This identification gives a description of a fusion category using a (possibly non-flat) bi-unitary connection, which arises as quantum 6j-symbols for a multi-fusion category.  We further advance this identification by working on the zipper condition, which is a kind of pentagon equation, and flat fields of strings.