Abstract
Polynomial systems naturally arise in many different contexts within mathematics, the sciences, and engineering. A central concept is discovering algorithms that will find all the isolated zeroes of a system. Systems that come from applications often have additional structure that cause a drop in the root count compared to the BKK bound. This talk will discuss a new algorithm that exploits the structure of a class of polynomial systems that have multiple common subexpressions which appear in the equations. This is joint work with B. Davis and J. Hauenstein.