Just to include something that starts to answer my own question Topological Quantum Computation Lecture notes covers a lot of the Mathematics of the Fractional Quantum Hall effect, or topological quantum computation. Such as Ribbon Categories, Modular functors, etc
Does anyone have other recommendations, for fusion algebras, the underlying representation theory,and quantum topology. Are Kevin Walkers TQFT notes good for instance?
I understand a lot of Chern Simons theory, but still have problems and most of CFT is alien to me.
So what are some good sources for the Mathematics of the Fractional Quantum Hall effect and Topological Quantum Computation. I appreciate however that the vast majority of the literature from a Mathematical point of view is in Topological Quantum Field Theories.
Audience: I'm a Mathematics Masters student with a BSc in Physics, so can stomach a fair bit of quantum mechanics. I do however find the literature on CFT to be intimitating!