In Section 3.iv, we saw that of the 12 rational cubics meeting 8 real points in the plane, at least 8 were real. This was the first instance of a non-trivial lower bound on the number of real solutions to a problem in enumerative geometry. Recent work of Eremenko and Gabrielov shows this phenomenon is pervasive in the Schubert calculus.

5. The Conjecture of Shapiro and Shapiro

- 6.i. Real Degree of Grassmann varieties
- 6.ii. Lower bounds in the Schubert calculus of flags?