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I have a somewhat unorthodox question. What are some good niche topics that aren't typically covered in courses in math to self-study? Ideally, I'm looking for something that could ultimately be useful in physics (even if it is rather advanced), but if not, I'm still open to suggestions.

My background: real analysis, advanced linear algebra, calculus on manifolds, complex analysis, differential equations, some functional analysis. I'm probably forgetting a few things.

Thanks!

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I don't know about "niche" topics but useful to physics: Lie theory, group theory, representation theory, differential geometry, PDEs... –  Ragib Zaman Dec 18 '12 at 4:38
    
Whats a niche, is that a candy bar –  Ethan Dec 18 '12 at 4:42
    
Hi Alex, maybe it helps if you have a look at the tags Chris Gerig uses on MathOverflow to see what mathematical topics are relevant and useful for physics. He is (as you, if I remember this correctly ?) interested in high energy physics theory too. –  Dilaton Dec 24 '12 at 22:18
    
And maybe it helps you getting a good answer, if you say here too, that you are finally interested in high energy physics theory and add some correspodning tags, such as mathematical-physics and/or string-theory; they exist here on Mathematics SE too. Happy holidays ;-) –  Dilaton Dec 24 '12 at 22:27

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