Frontiers of Arithmetic in Enumerative Geometry

The  Schubert calculus  of  enumerative geometry  is  a rich  and
well-understood  family  of  structured problems  in  enumerative
geometry.  With  many millions  of computable  problems, it  is a
laboratory  for   investigating  new  phenomena   in  enumerative
geometry.  I have been using it as  such for the past 25 years in
projects  to study  arithmetical questiions  (reality and  Galois
groups) in enumerative geometry and  more generally in systems of
equations.  These projects  use different computational resources
and well  over 15 TeraHertz-years  of computing.  This  talk will
sketch some  of the mathematics  and some of the  lessons learned
from these investigations.