Georgia Institute of Technology College of Sciences

Numerical algebraic geometry provides a collection of novel methods to treat the solutions of systems of polynomial equations. These hybrid symbolic-numerical methods based on homotopy continuation technique have found a wide range of applications in both pure and applied areas of mathematics. This talk gives an introduction to numerical algebraic geometry and outlines directions in which the area has been developing. Two topics are highlighted: (1) computation of Galois groups of Schubert problems, a recent application of numerical polynomial homotopy continuation algorithms to enumerative algebraic geometry; (2) numerical primary decomposition, the first numerical method that discovers embedded solution components.