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I'm a Mathematics masters student currently studying some aspects of TQFT. I'm interested in Langlands, mainly because it sounds oppressive! Is anyone familiar with any links between CFT and Langlands, or more importantly any readable intros to these sorts of areas.

How do Hecke Eigensheaves come into things? What does one need to know before hand. Are there any lists of requisite knowledge before tackling such concepts? Sometimes knowing where to start is a hard problem!

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    $\begingroup$ Did you mean to say "impressive" instead of "oppressive"? $\endgroup$
    – S. Carnahan ♦
    Commented Sep 1, 2011 at 17:27
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    $\begingroup$ Well, Scott, there are masochistic people who find oppressive things attractive :p $\endgroup$
    – Yuji Tachikawa
    Commented Sep 2, 2011 at 5:22
  • $\begingroup$ By the way, in number theory CFT = class field theory, which is the simplest (proved) instance of the Langlands program, so from that point of view asking about "links between CFT and Langlands" had me confused. I had to reread the question. $\endgroup$
    – KConrad
    Commented Sep 2, 2011 at 12:42

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There's a review article by Edward Frenkel which exactly fits your need: see "Lectures on the Langlands Program and Conformal Field Theory". It's posted on hep-th, but as I (as a string theorist) had difficulties reading it, it should be written for mathematicians :)

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