Title: Local Newforms and Supercuspidal Representations
Abstract: After reviewing some of the motivation coming from modular forms, we will discuss the modern, representation-theoretic perspective of local newforms. These are special vectors (up to scalars) inside many representations of certain p-adic groups. We will discuss what is known generally and then specialize to the case of supercuspidal representations. In particular, the cases of depth-zero and of "simple" supercuspidal representations will be covered in detail.