Lectures on Abundance Phenomena in Real Enumerative Geometry part 1

Surprisingly, in quite a number of real enumerative problems, the number of real solutions happens to satisfy high lower bounds. For the moment, such a phenomenon is rather deep studied in the following cases: in counting real lines and higher dimensional linear subspaces on projective hypersurfaces and complete intersections (a typical problem from a kind of Real Schubert Calculus); and in counting real rational curves interpolating real points on rational and K3 surfaces (a typical problem from a kind of Real Gromov-Witten Calculus).