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arXiv · 1109.3436

The monotone secant conjecture in the real Schubert calculus

Nickolas Hein·Christopher J. Hillar·Abraham Martin del Campo·Frank Sottile·Zach Teitler
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Abstract

The monotone secant conjecture posits a rich class of polynomial systems, all of whose solutions are real. These systems come from the Schubert calculus on flag manifolds, and the monotone secant conjecture is a compelling generalization of the Shapiro conjecture for Grassmannians (Theorem of Mukhin, Tarasov, and Varchenko). We present some theoretical evidence for this conjecture, as well as computational evidence obtained by 1.9 teraHertz-years of computing, and we discuss some of the phenomena we observed in our data.

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Nickolas Hein, Christopher J. Hillar, Abraham Martin del Campo, Frank Sottile, Zach Teitler. 2014-10-19. The monotone secant conjecture in the real Schubert calculus. https://arxiv.org/abs/1109.3436

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