English

The monotone secant conjecture in the real Schubert calculus

Algebraic Geometry 2014-10-21 v3

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.

Keywords

Cite

@article{arxiv.1109.3436,
  title  = {The monotone secant conjecture in the real Schubert calculus},
  author = {Nickolas Hein and Christopher J. Hillar and Abraham Martin del Campo and Frank Sottile and Zach Teitler},
  journal= {arXiv preprint arXiv:1109.3436},
  year   = {2014}
}

Comments

Final paper version of 2011 abstract for MEGA

R2 v1 2026-06-21T19:05:30.593Z