Midwest Algebra, Geometry and their Interactions Conference MAGIC05 University of Notre Dame, Notre Dame October 7-11, 2005 Parallel algorithms for a numerical irreducible decomposition by Jan VERSCHELDE, University of Illinois at Chicago Abstract: In collaboration with Andrew Sommese and Charles Wampler, homotopy continuation methods were developed to compute a numerical representation of all solutions of a polynomial system. Our numerical factorization algorithms to decompose a pure dimensional solution set into irreducible factors exploit monodromy group actions and use linear traces to certify an irreducible decomposition. We will present parallel factorization algorithms, developed recently with Anton Leykin.