Galois Groups for Systems of Equations

Camille Jordan observed that Galois groups arise in 
enumerative geometry, and we now also understand them
as monodromy groups. A study of this question in the
Schubert calculus has determined many such Galois groups,
all known Schubert Galois groups are either the full
symmetric group or are imprimitive.  Recently, Esterov considered 
this question for systems of sparse polynomials and proved 
this dichotomy in that setting.   While this classification 
identifies polynomial systems with imprimitive Galois groups, 
it does not identify the groups.  

I will sketch the background, before explaining Esterov's 
classification and ongoing work identifying some of the 
imprimitive Galois groups for polynomial systems.