Galois groups of Schubert problems

  The Galois group of a field extension encodes all of
its symmetries and it is the basic invariant of the
field extension.   Enumerative geometric problems, which
are fundamental in algebraic geometry, also have Galois
groups which encode the symmetries and the intrinsic 
structure of the geometric problem.

   These are, however, difficult to determine and hard
to study.   For a wide class of well-structured geometric 
problems (the Schubert Calculus) there are many approaches
and even some results.   My talk will introduce these
geometric Galois groups and discuss some of the approaches
to studying them and some of the results that we have 
obtained.   This is ongoing work with collaborators at 
other institutions and students at TAMU, including 
Abraham Martin del Campo and Chris Brooks.