TLDR: I know the basics of QFT and GR and looking to read IAS series on QFT and strings. I'm specifically looking for math or math for physicists books with exercises to study beforehand, the prerequisites to read these 2 volumes.
I'm about to start my PhD in mathematical physics, and I have read most parts of Schwartz and Wald in my masters. But since now I'm going more towards the theoretical side, I want to learn mathematics of it, not just in a scattered way around other textbooks but kind of structured way. In this regard, I've learnt basic measure theory, algebra, point set topology and functional analysis as a start, and now I want to go to the algebraic topology/differential topology/differential geometry/algebraic geometry side of things.
My advisor suggested to me that if I have time, I go on and learn these subjects from math books, but he is a bit old and his recommendations seem impossible to complete in a reasonable amount of time. (for example: he suggested I read Hartshorne for AG).
So, I came here for advice, I'm hoping to learn string theory as an end goal, in that regard, after completing something like GSW or Polchinski, I want to read the IAS lectures to get a solid ground in mathematical side of things. So, to an extent, I want to know a list of math books that would let me read these books. I am asking this in a single question because so many of the "math for physics" books do cover some of these topics simultaneously.
I also want these books to contain exercises because I will be mostly going through them myself. (Something like Nakahara, where there are very little number of problems also don't work for me)
So, what would be the recommendations? and if possible, can you give me an order to read? I know that the usual math order is top -> diff geo (lie stuff)-> AG but as I've said, if you're going to recommend me math for physics books, they tend to mix things up a bit.
I also checked out other math for physics questions, but couldn't reach a conclusion.
