Mathematics and Physics prerequisites for mirror symmetry

Question

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.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user ramanujan_dirac

Comments

I guess somebody who wants to write an answer here has to be fast, for unfortunately well known reasons ... :-/

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton

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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.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user user1504

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@user1504: I am not looking for a specific list of topics, but rather general prerequisites, and some references that I can browse. e.g. you gave Hori.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user ramanujan_dirac

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A PDF of the Hori is the first hit when I google 'mirror symmetry book'.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user user1504

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This might be the sort of thing to ask about in Physics Chat.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user David Z

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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.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton

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I dont know why David always does this, it looks very strange to me and not at all like a fair and even-handed moderation practice. So I have flagged the question because of this such that the other moderators of the site can have a look at it. If this keeps going I should probably write a mail at Anna Lear.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton

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Somewhat related: physics.stackexchange.com/q/2528/2451

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Qmechanic

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@Qmechanic thanks for finding and providing this link, this should be helpful for many people having their similar questions closed without answer.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton

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@Dilaton: You could nominate it for reopening?

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user ramanujan_dirac

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@ramanujan_dirac I unfortunately do not have 3000 rep, so I can not vote for reopen. In addition, it would be good to have some other (theoretically interested) people with enough rep at our side, since if I have this right 5 people (without the help of a mod who could reopen it immediately) are needed. I said it should be reopend in my flag, but as expected that flag was almost immediatelly declined. I hope the link Qmechanic has found helps a little bit. Qmechanic would maybe have left the question allone ...

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton

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@Dilaton: I guess this question could find a better receiving audience at Math SE or MO.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user ramanujan_dirac

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@ramanujan_dirac as I have observed from my limited hanging around at maths, they rather apply a "what is helpful to the community is good" approach to decide what is an allowed question, conversely to here. Not sure if they would think it is too related to this they already have. Maybe you should be a bit careful because cross posisting is not always appreciated. But if you say that it is closed here because of differences in policy, maybe you would be lucky. Worse than what happend here (closed) it can not get I think

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton

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With the policy on MO I am less familiar. I have just noted that they are, even though it is a math site, obviously quite interested in mathematical and theoretical physics too. If the moderator stile is similar to the formar Theoretical Physics SE, they would give you answers or at least nice hints and advice how to proceed, instead of just closing the question. If I got a question closed that is very important for me, I would probably try it somewhere else.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton

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@Dilaton I close these questions because they're off topic, as determined in the meta discussion you linked to. Information about mathematical prerequisites goes in the tag wikis, not in questions. That's not unfair or biased.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user David Z

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@DavidZaslavsky Nobody writes useful tagwikis. Without wanting to repeat the whole discussion, this does not work, we have a catch 22. People who have to decide, including you, do not care about this or my constructive suggestions about how to avoid the catch 22, and the only big loosers of this situation are people such as ramanujan_dirac and others who will never get the information they need. The only one who did something nice and helpful is Qmechanic by finding the link.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton

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The people who decided on the meta post are obviously not the ones interested in such information, so they dont care if what they decided does work or not. Maybe it would really be best for people who are interested in that information (and the corresponding physics topics) just go to Maths SE or MO ... These topics revolving around theoretical high energy physics for example are dying out here anyway. Ramanujan_dirac is among the last few people still asking questions about such advanced topics, so I guess it will not matter for too long anymore if the information people need can be found.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton

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BTW it strikes me odd that you never wait for 3 or 4 close votes to accummulat on such questions, or wait to see if other people (who are not active on meta and have not seen the meta post, I am sure ramanujan_dirac and the other people who do want to know did not take part in the meta discusssion) would say leave open or not ...

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton

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Just saying "all these informations should go into the tagwikis" as I know well people who took part in the meta discussion agreed upon even though it obviously does not work (I predicted this in on meta and stated the problem) is among the things I critisizes as applying political rules without thinking (reasonably and clear headed) about it.

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton

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@Qmechanic since you have reviewed this question (probably appearing in the reopen queue because of a reopen vote?) as "leave closed", it would be nice if you could write down the information asked for in this question, or more generally the mathematical prerequisits needed to learn string theory together with some useful links, into the tagwiki. I know you could do this if you wanted too ...

This post imported from StackExchange Physics at 2014-07-09 07:36 (UCT), posted by SE-user Dilaton