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Real Solutions to Equations from Geometry
About this Title
Frank Sottile, Texas A&M University, College Station, TX
Publication: University Lecture Series
Publication Year:
2011; Volume 57
ISBNs: 978-0-8218-5331-3 (print); 978-1-4704-1652-2 (online)
DOI: https://doi.org/10.1090/ulect/057
MathSciNet review: MR2830310
MSC: Primary 14P05; Secondary 12D10, 14M15, 14N10, 14P25
Table of Contents
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Front/Back Matter
Chapters
- 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