Galois groups in Enumerative Geometry
 
    In 1870 Jordan explained how Galois theory can be applied
 to problems from enumerative geometry, with the group
 encoding intrinsic structure of the problem.  Earlier
 Hermite showed the equivalence of Galois groups with
 geometric monodromy groups, and in 1979 Harris initiated the
 modern study of Galois groups of enumerative problems.  He
 posited that a Galois group should be `as large as possible'
 in that it will be the largest group preserving internal
 symmetry in the geometric problem.

   I will describe this background and discuss some work of
 many to compute, study, and use Galois groups of geometric
 problems, including those that arise in applications of
 algebraic geometry.