## Student Number Theory Seminar 2019-20

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10/7/19: Katy Weber -- *A Tour of the p-adic Representation Theory of GL_2*

**Abstract:** We summarize the classification of representations of GL_2 over a p-adic field, emphasizing the relationship between these representations and automorphic forms and L-functions. Time permitting, we will also discuss Whittaker models of these representations and the Casselman-Shalika formula. This talk is meant to be a sketch of these results and how they fit into the bigger picture, and should be accessible even if you are not very familiar with representation theory.