Oh cry me a god-damned river. I was expected to know real and complex analysis, even though my work was in modular representation theory.pic.twitter.com/oXsrCijiEu
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Apparently it runs deep in the Langlands program though. http://www.math.harvard.edu/~chaoli/doc/EilenbergLectures.html …
And of course there's a ton of complex analysis in Langlands too! Good thing they made me study it, right?
Heh, "Langlands program" is always the answer. :-) But messy Diophantine eqs -> anabelian stuff -> current rep. theory fails?
Oh no. Representation theory doesn't care much about commutative vs. non.
But it's very sensitive to the base field. "Ordinary" = "over the complex numbers". "Modular" = characteristic p.
Modular representation theory is vastly, vastly harder.
Like: a big ordinary representation theory question would be "find the representations of the Monster group"
My dissertation was done over the group Z/p x Z/p of order p^2. And actually mostly over Z/3 x Z/3.
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