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

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.)

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

Any other advice regarding how should I proceed.

Sorry for such a long post and Thank you in advance