TY - JOUR
T1 - The monotone secant conjecture in the real schubert calculus
AU - Hein, Nickolas
AU - Hillar, Christopher J.
AU - Martin Del Campo, Abraham
AU - Sottile, Frank
AU - Teitler, Zach
N1 - Publisher Copyright:
© Taylor and Francis Group, LLC.
PY - 2015/7/3
Y1 - 2015/7/3
N2 - 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.
AB - 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.
KW - Schubert calculus
KW - Shapiro conjecture
KW - flag manifold
UR - https://www.scopus.com/pages/publications/84932621392
U2 - 10.1080/10586458.2014.980044
DO - 10.1080/10586458.2014.980044
M3 - Article
AN - SCOPUS:84932621392
SN - 1058-6458
VL - 24
SP - 261
EP - 269
JO - Experimental Mathematics
JF - Experimental Mathematics
IS - 3
ER -