Solving polynomial systems by polyhedral homotopy

Prof. T.Y. Li

Department of Mathematics Michigan State University, East Lansing, Michigan

Recently, a major computational breakthrough has emerged in solving polynomial systems by the homotopy continuation method. The Bernstein theory in combinatoial geometry comes to provide a much tighter bound of the root count, usually measured by the Bezout number. When this bound is employed in the homotopy algorithm, a great amount of computation is saved. The basic idea will be presented in this talk.