## 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.