Patrick Hooper (City College New York)
The extrinsic primitive torsion problem

We consider images of the free group F with two generators where images of all primitive elements have order k, for some positive integer k. We are interested in questions like when (in terms of k) the image must be finite, finitely generated, nilpotent, etc. Geometric motivation comes from understanding square tiled surfaces (punctured torus covers with a flat structure). I'll explain what we are able say about the answers to these questions, discuss the techniques we use, and mention some interesting open questions. This is joint work with Khalid Bou-Rabee.
Degenerate Whittaker Models for Cuspidal Representations of GL(kn,F)