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What are the topics that should be mastered by someone who wants to understand geometric computational complexity?

Surely, a lot of algebraic geometry and representation theory are needed, but which topics? and representation theory of what? groups, lie algebras etc? naming good resources ( texts etc ) that cover this background will be highly appreciated.

I'm not sure if this question should be asked here in math.se or in theoretical computer science forum, so if you find it more useful to post it there, please tell me.

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  • $\begingroup$ MathsLover, I see that you have created (geometric-complexity) tag. It might be useful to create also tag-wiki or at least tag-excerpt. It might help other users to use the tag correctly. Another reason is that the tags used on only one question are automatically deleted after certain time unless they have tag-wiki. $\endgroup$ Dec 28, 2016 at 17:17
  • $\begingroup$ @MartinSleziak, I've added an excerpt but I don't know if it's the best one to provide. but It's in the process of being peer-reviewed. $\endgroup$
    – FNH
    Dec 28, 2016 at 22:37
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    $\begingroup$ I saw that you edit was rejected. I have edited the text from your suggestion into the tag-info. $\endgroup$ Dec 29, 2016 at 6:49

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I took a course with Mulmuley on GCT. I think the main topics to be familiar with are

  • representation theory of the symmetric group
  • representation theory of $\mathrm{GL}_n \mathbb{C}$
  • geometric invariant theory

Fulton and Harris is good for the rep theory (or google around for notes). I guess Mumford's book is the standard for geometric invariant theory (GIT) though frankly I don't know much about it. The basic setting of GIT is algebro-geometric so some knowledge of the basic objects of algebraic geometry would be required.

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  • $\begingroup$ I'd like to know which monographs and sources did you use in the course for the study and how much knowledge of the background are needed to start studying GCT? Thank you very much :) $\endgroup$
    – FNH
    Dec 24, 2016 at 15:20

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