Talk, Oxford University, Oxford, UK
Bosonization is an example of a duality—it relates fermions and bosons in 1+1d. In my talk, I will describe the bosonization formalism, in particular, I will motivate and offer a heuristic derivation (without detailed proof) of the bosonization identity. I will follow the constructive approach of van Delft and Schoeller. As an application of the formalism, I will explain the connection to Luttinger liquids.
Talk, Oxford University, Oxford, UK
I will talk about the Haldane model for the Quantum Anomalous Hall Effect and the Kane and Mele model for the Quantum Spin Hall Effect. I will then discuss the relation between topological insulators and anomalies and the theta-term.
Talk, Oxford University, Oxford, UK
I will introduce the Ising gauge theory as the simplest example of a lattice gauge theory. I will discuss the physical observables in this model before moving on to describe the phase diagram. Along the way we will discover a duality to the transverse field Ising model and the topological aspects of this model.
Talk, Oxford Univeristy, Oxford, UK
An introduction to categpry theory for physicists and the formulation of TQFTs in this language.
Talk, Oxford University, Oxford, UK
An overview of the TKNN invariant and the connection to the mathematics of fibre bundles.