Function theory on the Neil parabola
  We give a formula for the Carath\'eodory distance on the Neil parabola, the variety ${z^2=w^3}$ restricted to the bidisk; thus making it the first variety with a singularity to have its Carath\'eodory distance explicitly computed. In addition, we relate this to a mixed Carath\'eodory-Pick interpolation problem for which known interpolation theorems do not apply. Finally, we prove a bounded holomorphic function extension result from the Neil parabola to the bidisk. 
Greg Knese