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Experimentation and conjectures in the real Schubert calculus for flag manifolds

James Ruffo·Yuval Sivan·Evgenia Soprunova·Frank Sottile
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Abstract

The Shapiro conjecture in the real Schubert calculus, while likely true for Grassmannians, fails to hold for flag manifolds, but in a very interesting way. We give a refinement of the Shapiro conjecture for the flag manifold and present massive (15.76 gigahertz-years) computational experimentation in support of this refined conjecture. We also prove the conjecture in some special cases using discriminants and establish relationships between different cases of the conjecture.

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James Ruffo, Yuval Sivan, Evgenia Soprunova, Frank Sottile. 2005-11-22. Experimentation and conjectures in the real Schubert calculus for flag manifolds. https://arxiv.org/abs/math/0507377

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