IMA Postdoc Seminar (February 8, 2008)

Speaker: Anton Leykin (IMA)

Title: Applications of numerical algebraic geometry

Abstract: Numerical Algebraic Geometry provides a collection of new methods to treat the solutions of systems of polynomial equations. The numerical homotopy continuation technique forms a base for higher level algorithms in the area.

This talk exposes three topics. First is a recent application of homotopy continuation to a problem in enumerative algebraic geometry: computation of Galois groups of Schubert problems. Second is a deflation method that restores the convergence of the Newton's method at a singular isolated solution of a polynomial system. Third is a new approach to detecting embedded components of an underlying complex variety dubbed numerical primary decomposition.