Mod p representations in the Langlands program

At least the first half of this talk will be a gentle introduction to the Langlands program, accessible to first-year graduate students with an interest in number theory and representation theory. In the second half I will discuss the 'automorphic' side of a mod p variant of the local Langlands correspondence, where derived methods are prevalent. At the very end I hope to give a rough sketch of various results obtained jointly with Peter Schneider. 

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