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## 5. The Conjecture of Shapiro and Shapiro

The results of Section 4 were inspired by a
remarkable conjecture of Boris Shapiro and Michael Shapiro.
We discuss that conjecture and its extensions in this Section.
There is a separate Web page
discussing this conjecture, and everything known about it in 1999.
We highly recommend its perusal.
4. The Schubert Calculus

- 5.i. The Conjecture of Shapiro and Shapiro for
Grassmannians
- 5.ii. Rational functions with real critical points
- 5.iii. Extensions of the Conjecture of Shapiro

6. Lower Bounds in the Schubert Calculus

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