Georgia Institute of Technology College of Sciences

Numerical algebraic geometry revolves around the study of solutions to polynomial systems via numerical method. Two of the fundamental tools in this field are the polyhedral homotopy of Huber and Sturmfels for computing isolated solutions and the concept of witness sets put forth by Sommese and Wampler as numerical representations for non-isolated solution components. In this talk, we will describe a stratified polyhedral homotopy method that will bridge the gap between these two largely independent area. Such a homotopy method will discover numerical representations of non-isolated solution components as by-products from the process of computing isolated solutions. We will also outline the pipeline of numerical algorithms necessary to implement this homotopy method on modern massively parallel computing architecture.