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Experimental Mathematics Volume 9, 2000 - Issue 2
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Original Articles

Real Schubert Calculus: Polynomial Systems and a Conjecture of Shapiro and Shapiro

Frank Sottile Department of Mathematics and Statistics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, MA, 01003, United States E-mail: [email protected]  http://www.math.umass.edu/-sottile
Pages 161-182 | Published online: 04 Apr 2012

Citations (20)

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Read on this site (3)

Nickolas Hein, Christopher J. Hillar, Abraham Martín del Campo, Frank Sottile & Zach Teitler. (2015) The Monotone Secant Conjecture in the Real Schubert Calculus. Experimental Mathematics 24:3, pages 261-269.
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LuisD. García-Puente, Nickolas Hein, Christopher Hillar, Abraham Martín del Campo, James Ruffo, Frank Sottile & Zach Teitler. (2012) The Secant Conjecture in the Real Schubert Calculus. Experimental Mathematics 21:3, pages 252-265.
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Jan Verschelde. (2000) Numerical Evidence for a Conjecture in Real Algebraic Geometry. Experimental Mathematics 9:2, pages 183-196.
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Articles from other publishers (17)

Steven N. Karp. (2023) Wronskians, total positivity, and real Schubert calculus. Selecta Mathematica 30:1.
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Yilin Wang. (2022) Large deviations of Schramm-Loewner evolutions: A survey. Probability Surveys 19:none.
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Victor Magron & Mohab Safey El Din. (2021) On exact Reznick, Hilbert-Artin and Putinar's representations. Journal of Symbolic Computation 107, pages 221-250.
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Yazdan Bavafa-Toosi. 2019. Introduction to Linear Control Systems. Introduction to Linear Control Systems 847 974 .
Nickolas Hein & Frank Sottile. (2017) A lifted square formulation for certifiable Schubert calculus. Journal of Symbolic Computation 79, pages 594-608.
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Bernd Sturmfels. 2017. Combinatorial Algebraic Geometry. Combinatorial Algebraic Geometry 1 19 .
Jonathan D. Hauenstein, Nickolas Hein & Frank Sottile. (2015) A Primal-Dual Formulation for Certifiable Computations in Schubert Calculus. Foundations of Computational Mathematics 16:4, pages 941-963.
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Monique Azar & Andrei Gabrielov. (2010) Some Lower Bounds in the B. and M. Shapiro Conjecture for Flag Varieties. Discrete & Computational Geometry 46:4, pages 636-659.
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Alexandre Eremenko & Andrei Gabrielov. 2011. Notions of Positivity and the Geometry of Polynomials. Notions of Positivity and the Geometry of Polynomials 167 178 .
Kevin Purbhoo. (2010) Jeu de taquin and a monodromy problem for Wronskians of polynomials. Advances in Mathematics 224:3, pages 827-862.
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Frank Sottile. (2009) General isotropic flags are general (for Grassmannian Schubert calculus). Journal of Algebraic Geometry 19:2, pages 367-370.
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Evgeny Mukhin, Vitaly Tarasov & Alexander Varchenko. (2009) The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz. Annals of Mathematics 170:2, pages 863-881.
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V. SEDYKH & B. SHAPIRO. (2012) ON TWO CONJECTURES CONCERNING CONVEX CURVES. International Journal of Mathematics 16:10, pages 1157-1173.
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Karin Gatermann & Pablo A. Parrilo. (2004) Symmetry groups, semidefinite programs, and sums of squares. Journal of Pure and Applied Algebra 192:1-3, pages 95-128.
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A. Eremenko & A. Gabrielov. (2002) Counterexamples to pole placement by static output feedback. Linear Algebra and its Applications 351-352, pages 211-218.
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A. Eremenko & A. Gabrielov. (2002) Pole Placement by Static Output Feedback for Generic Linear Systems. SIAM Journal on Control and Optimization 41:1, pages 303-312.
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Frank Sottile. 2002. Computations in Algebraic Geometry with Macaulay 2. Computations in Algebraic Geometry with Macaulay 2 101 129 .

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