I am a physics undergrad interested in Mathematical Physics. I am more interested in the mathematical side of things, and interested to solve problems in mathematics inspired by physics maybe with the help of techniques in Physics.

My current knowledge is some QFT(beginnings of QED), no string theory, differential geometry confined to riemannian manifolds, and some knowledge on Riemann surfaces.

One such area is Mirror Symmetry. What are the QFT and string theory prerequisites, and also how much algebraic geometry and topology should I know (is this confined to complex manifolds)?

Also books and references which build up this background, and also directly on mirror symmetry would be appreciated.