Schubert Galois Groups

Problems from enumerative geometry have Galois groups.  Like those from
field extensions, these Galois groups reflect the internal structure of
the original problem.  The Schubert calculus is a class of problems in
enumerative geometry that is very well understood, and may be used as a
laboratory to study new phenomena in enumerative geometry.

I will discuss this background, and sketch a picture that is emerging
from a sustained study of Schubert problems from the perspective of
Galois theory.  This includes a conjecture concerning the possible
Schubert Galois groups, a partial solution of the inverse Galois problem,
as well as glimpses of the outline of a possible classification of
Schubert problems for their Galois groups.