Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres. Perimeter now has 7 formal presentation spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities. Recordings of events in these areas are all available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA). PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.
I will describe a framework for the study of symmetry-enriched topological order using graded matrix product operator algebras. The approach is based upon an explicit construction of the extrinsic symmetry defects, which facilitates the extraction of their physical properties. This allows for a simple analysis of dual phase transitions, induced by gauging a global symmetry, and condensation of a bosonic subtheory.
I will discuss some (higher-)categorical structures present in three-dimensional topological field theories that include topological defects of any codimension. The emphasis will be on two topics:
(1) For Reshetikhin-Turaev type theories, regarded as 3-2-1-extended TFTs, I will explain why codimension-1 boundaries and defects form bicategories of module categories over suitable fusion categories.
In 1977, Blandford and Znajek discovered a process by which a spinning
black hole can transfer rotational energy to a force-free plasma, offering a possible mechanism for energy and jet emissions from quasars and other astrophysical sources. This Blandford-Znajek (BZ) mechanism is a Penrose process, which exploits the presence of an ergosphere supporting negative energy states, and it involves currents of electrical charge sourcing the toroidal magnetic field component of the emitted Poynting flux.
We show that Kitaev's lattice model for a finite-dimensional semisimple Hopf algebra H is equivalent to the combinatorial quantisation of Chern-Simons theory for the Drinfeld double D(H). As a result, Kitaev models are a special case of combinatorial quantization of Chern-Simons theory by Alekseev, Grosse and Schomerus. This equivalence is an analogue of the relation between Turaev-Viro and Reshetikhin-Turaev TQFTs and relates them to the quantisation of moduli spaces of flat connections.
A variety of models, especially Kitaev models, quantum Chern-Simons theory, and models from 3d quantum gravity, hint at a kind of lattice gauge theory in which the gauge group is generalized to a Hopf algebra. However, until recently, no general notion of Hopf algebra gauge theory was available. In this self-contained introduction, I will cover background on lattice gauge theory and Hopf algebras, and explain our recent construction of Hopf algebra gauge theory on a ribbon graph (arXiv:1512.03966).
I will discuss the relation between topological field theories and gapped phases of matter. I will propose a general formalism to define a class of TFTs which can be realized by commuting projector Hamiltonians. This allows one to apply rigorous mathematical theorems about TFTs to gapped phases of matter. I will also discuss the role of generalized cohomology theories and spectra in the classification of SPT phases.
The (Freedman-Kitaev) topological model for quantum computation is an inherently fault-tolerant computation scheme, storing information in topological (rather than local) degrees of freedom with quantum gates typically realized by braiding quasi-particles in two dimensional media. I will give an overview of this model, emphasizing the mathematical aspects.
The aim of this talk is to give an introduction to modular categories, touching both basics and recent developments. I will begin with a quick reminder concerning tensor categories, in particular braided and symmetric ones, and notions like duality, fusion and spherical categories. We'll meet algebras in tensor categories, categories of modules, module categories and their connection. I will then focus on modular categories and some basic structure theory. We will consider two ways of obtaining modular categories: modularization and the Drinfeld center.
IT from Qubit web seminar
I will give an introduction to the Kitaev quantum double models for Hopf C*-algebras. To this end I will introduce a graphical tensor-network notation to represent the algebraic objects and axioms. Using this notation I will then present the vertex- and plaquette symmetries of the model and discuss their interaction and the excitation structure they give rise to.
Check back for details on the next lecture in Perimeter's Public Lectures Series