Complex enumerative geometry deals with counting algebraic-geometric
objects satisfying certain restrictions, e.g. counting a number of
algebraic curves of a fixed degree passing through a fixed set of
points and tangent to some fixed algebraic curves.
I will discuss a real counterpart of such problems, where some objects
may be taken smooth instead of rigid algebraic and one counts curves
with signs. I will then explain a relation of these problems with the
theory of finite type invariants and propose a general setting to
produce such invariants (using evaluation maps of configuration spaces
and homology intersections).