I will discuss some approaches to the problem of constructing and characterizing uniqueness polynomials and unique range sets. For uniqueness polynomials I will discuss a method to explicitly construct regular 1-forms on singular curves associated to the polynomials, and in the case of unique range sets I will explain how a method of Siu can be used to construct examples of unique range sets coming from uniqueness polynomials P without assuming an injectivity condition on the zeros of the derivative P'.

Fields Institute, Stewart Library