article published yes Nicolas Hein author Christopher Hillar author Abraham Martin Del Campo Sanchez author 4CF47F6A-F248-11E8-B48F-1D18A9856A87 Frank Sottile author Zach Teitler author CaUh department 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. Taylor & Francis2015 eng 1109.3436 00035687390000110.1080/10586458.2014.980044 243261 - 269 Hein, Nicolas, Christopher Hillar, Abraham Martin del Campo Sanchez, Frank Sottile, and Zach Teitler. “The Monotone Secant Conjecture in the Real Schubert Calculus.” <i>Experimental Mathematics</i>. Taylor &#38; Francis, 2015. <a href="https://doi.org/10.1080/10586458.2014.980044">https://doi.org/10.1080/10586458.2014.980044</a>. Hein, Nicolas, et al. “The Monotone Secant Conjecture in the Real Schubert Calculus.” <i>Experimental Mathematics</i>, vol. 24, no. 3, Taylor &#38; Francis, 2015, pp. 261–69, doi:<a href="https://doi.org/10.1080/10586458.2014.980044">10.1080/10586458.2014.980044</a>. Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. 2015. The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics. 24(3), 261–269. Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. The monotone secant conjecture in the real Schubert calculus. <i>Experimental Mathematics</i>. 2015;24(3):261-269. doi:<a href="https://doi.org/10.1080/10586458.2014.980044">10.1080/10586458.2014.980044</a> N. Hein, C. Hillar, A. Martin del Campo Sanchez, F. Sottile, and Z. Teitler, “The monotone secant conjecture in the real Schubert calculus,” <i>Experimental Mathematics</i>, vol. 24, no. 3. Taylor &#38; Francis, pp. 261–269, 2015. N. Hein, C. Hillar, A. Martin del Campo Sanchez, F. Sottile, Z. Teitler, Experimental Mathematics 24 (2015) 261–269. Hein, N., Hillar, C., Martin del Campo Sanchez, A., Sottile, F., &#38; Teitler, Z. (2015). The monotone secant conjecture in the real Schubert calculus. <i>Experimental Mathematics</i>. Taylor &#38; Francis. <a href="https://doi.org/10.1080/10586458.2014.980044">https://doi.org/10.1080/10586458.2014.980044</a> 20062018-12-11T11:55:10Z2025-09-23T14:07:49Z