I'm interested in learning more about the mathematical structure underneath of quantum field theory and string theory. I've taken a few courses on quantum field theory before, so am getting more comfortable with the topic. Hence my desire to learn about it's structure in a little more mathematical depth. In particular, I am after a set of notes, textbook, or survey which doesn't shy away from the maths. I was pointed towards Quantum Fields and Strings: A Course for Mathematicians by Witten, Deligne, et al.
Having taken a glance at the notes, it looks like just what I am after. However it also looks like it has some fairly heavy mathematical prerequisites.
In quite a few areas of math I'm still get to go beyond an introductory course (e.g. algebraic topology, algebraic geometry, symplectic geometry, etc). I am happy to brush up and improve my knowledge in such fields, but there is no preface suggesting what topics or what level is expected of the reader.
It would be appreciated if someone could take a skim through the text and try to list the mathematical topics that are prerequisites, and give an indication of how well that topic should be understood (e.g. basics of algebraic topology enough? or significant algebraic topology required?).