I will introduce a few ideas and concepts around the theme of
"orientifolds", a generalization of manifolds to the point of view of
unoriented extended objects probing them.
This provides an intriguing
connection between spacetime geometry, the geometry of the extended
object, and the geometry of moduli space.
I will speculate why the recent
application of string theory techniques in condensed matter physics may
evolve to involve orientifold techniques.