Includes bibliographical references (p. 189-194) and index

Chapter 1. Overview Chapter 2. Real solutions of univariate polynomials Chapter 3. Sparse polynomial systems Chapter 4. Toric degenerations and Kushnirenko's theorem Chapter 5. Fewnomial upper bounds Chapter 6. Fewnomial upper bounds from Gale dual polynomial systems Chapter 7. Lower bounds for sparse polynomial systems Chapter 8. Some lower bounds for systems of polynomials Chapter 9. Enumerative real algebraic geometry Chapter 10. The Shapiro Conjecture for Grassmannians Chapter 11. The Shapiro Conjecture for rational functions Chapter 12. Proof of the Shapiro Conjecture for Grassmannians Chapter 13. Beyond the Shapiro Conjecture for the Grassmannian Chapter 14. The Shapiro Conjecture beyond the Grassmannian

Access is restricted to licensed institutions

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012