Peter Humphries (University of Virginia): Newform theory for $\mathrm{GL}_n$

Abstract: We shall discuss three interrelated notions in the theory of automorphic forms and automorphic representations: newforms, $L$-functions, and conductors. In particular, we cover how to define the newform associated to an automorphic representation of $\mathrm{GL}_n$, how to realise certain $L$-functions as period integrals involving newforms, and how to quantify the ramification of an automorphic representation in terms of properties of the newform.

The link for the talk is https://zoom.us/j/94752830725, the password is the order of $\mathrm{SL}_2(\mathbb{F}_{97})$.