6. Lower Bounds in the Real Schubert calculus

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?