Guidance regarding research in Mathematical Physics

Question

I am currently a Master's student in Mathematics. The main focus of my undergraduate programme was on Mathematics. However as a part of the course, I have done some Theoretical Physics courses. In mathematics, my area of interest is Topology-Geometry and I also like analysis. I have heard recently lots of exciting research is going on at the intersection of Top-Geo and QFT/String Theory (for example Witten's work/ Yang-Mills theory) and Mathematical Foundations of QFT etc. I am very eager to learn them/do my doctoral work in this direction (in some mathematics department). I shall highly appreciate any comment/guidance/advice in this direction. For example

1. Can you please tell me name of some good books/lecture notes/lecture videos from where I can learn QFT, GR, Gauge Theory, String theory from a physicist's view point so that I get enough motivation/intuition to read books where they have been discussed with a greater mathematical sophistication? (I have downloaded quite a lot of books written in this direction including Quantum fields and Strings- A course for mathematicians, but unfortunately I cannot read any of them.)

2. Can you tell me name of some mathematics department with an active Mathematical Physics research group?

3. Any other advice regarding how should I proceed.

Sorry for such a long post and Thank you in advance

Answer 1

I am also a mathematics student who likes physics. My advice would be:

• I learned a bit of QFT following Srednicki's book and Tong's lecture notes. A note: the book focuses mainly on the path integral approach, with very little in the way of S-matrix techniques.
• For GR, I found Jetzer's lecture notes and, knowing the guy, Graf's lecture notes ought to be great.
• I have learned String theory on some book, but I don't remember the title right now. If you want can look it up.

I think here at ETH there's a pretty good group doing mathematical physics, if you want to try to apply and to move to Switzerland.

Also general advice: If you are interested in a topic in physics, always look if Tong has written something on it. His lecture notes are usually very good.