The Monotone Secant Conjecture in the real Schubert calculus

Details The Monotone Secant Conjecture in the real Schubert calculus The Monotone Secant Conjecture in the real Schubert calculus

2011-09-15

arxiv.org/abs/1109.3436v1

Mathematics

Algebraic Geometry

Extended abstract presented in MEGA 2011

Scientific paper

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 the Monotone Secant Conjecture, explain the massive computation evidence in its favor, and discuss its relation to the Shapiro Conjecture.

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