Solving Sparse Decomposable Systems

Esterov classified the monodromy/Galois groups of sparse systems of 
polynomials---they are either full symmetric or imprimitive, and
when imprimitive there is a recursive structure, reducing them
to systems that are full symmetric.  We first show how the total space of 
solutions to systems with imprimitive monodromy is a sequence of 
decomposable projections in the sense of Amendola et al., corresponding
to Esterov's recursive structure.   We show how to exploit this structure 
to reduce solving an imprimitive system of sparse polynomails to solving 
a sequence of much smaller systems of polynomials with symmetric monodromy.

I will explain these structures and this work, which is joint with
Brysiewicz, Rodriguez, and Yahl, and present computational results
of an implementation of this algorithm in Macaulay 2.