Speaker: Liang Kong (Univ. New Hampshire/Harvard Univ.)

Title: Lattices models for topological orders and boundary-bulk duality

Time/Date: 4:45-6:15, Monday, June 13, 2016,

Room: 118

Abstract: In this talk, I will explain how to construct lattice models that can realize 2+1D topological phase of matters (or topological orders) and how to define and classify topological excitations in these models. This classification relies on an explicit construction of a local operator algebra, which turns out to be a weak C*-Hopf algebra. A topological excitation is a module over this algebra. In these models, I will prove the so-called boundary-bulk duality, the part of which says that all boundary excitations form a unitary fusion category and all bulk excitations form its Drinfeld center. The complete duality says that there is a fully faithful boundary-to-bulk functor given by taking centers. This duality is not an isolated phenomena. It also appeared in the study of rational conformation field theories. So this is natural to ask how general it is. If time permits, I will talk about my recent works on how to generalize this duality to higher dimensional topological orders.