The Monotone Secant Conjecture in the Real Schubert Calculus
The Monotone Secant Conjecture in the Real Schubert Calculus
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 …