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 using 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 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.

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    $\begingroup$ You seem to be imagining that we can give you a list of topics to master, and then you'll be ready for mirror symmetry. But mirror symmetry is a large and active field of research, constantly changing. What's important to know could change the next time Kontsevich blows his nose. Which means, IMHO, that you are asking a question whose answer is not defined. I suggest that, instead of waiting for us to tell you what to do, you browse through a few books on mirror symmetry, choose one that looks likely (maybe Hori et al?), and then come back and ask conceptual questions when you get stuck. $\endgroup$
    – user1504
    Feb 25 '13 at 15:11
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    $\begingroup$ This might be the sort of thing to ask about in Physics Chat. $\endgroup$
    – David Z
    Feb 25 '13 at 18:50
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    $\begingroup$ Whereas it is sometimes allowed to ask about (mathematical) prerequisits to study certain things such as relativity, quantum mechanics, or Maxwells equations, David Zalsavsky closes every question of people who want to know about prerequisits to study string theory or things too closely related. This is very biased, unfair, and annoying. $\endgroup$
    – Dilaton
    Feb 25 '13 at 19:23
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    $\begingroup$ Somewhat related: physics.stackexchange.com/q/2528/2451 $\endgroup$
    – Qmechanic
    Feb 25 '13 at 20:41
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    $\begingroup$ @Dilaton: I guess this question could find a better receiving audience at Math SE or MO. $\endgroup$
    – user7757
    Feb 25 '13 at 22:47