Enumerative Real Algebraic Geometry
Frank Sottile
sottile@tamu.edu
4 August 2002
2000 Mathematics Subject Classification
14P99, 12D10, 14N10, 14N15, 14M15, 14M25, 14M17
Table of Contents
Summary
- Introduction
- Polynomial Systems
- Sparse Polynomial Systems
- The Polyhedral Homotopy Algorithm
- Real Solutions to Sparse Polynomial Systems
- Enumerative Real Algebraic Geometry
- Enumerative Real Algebraic Geometry
- Problems not involving general conditions
- The Stewart-Gough Platform
- Real rational cubics through 8 points in
R2
- Common tangent lines to Spheres in
Rn
- Schubert Calculus
- The Schubert Calculus of Lines
- The Special Schubert Calculus
- Further Extensions of the Schubert Calculus
- The Conjecture of Shapiro and Shapiro
- The Conjecture of Shapiro and Shapiro for Grassmannians
- Rational functions with real critical points
- Extensions of the Conjecture of Shapiro
- Lower Bounds in the Schubert calculus
- Real Degree of Grassmann varieties
- Lower bounds in the Schubert calculus of flags?
- Acknowledgements
- Bibliography