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Experimentation and conjectures in the real Schubert calculus for flag manifolds (extended abstract)

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

The Shapiro conjecture in the real Schubert calculus fails to hold for flag manifolds, but in a very interesting way. In this extended abstract, we give a refinement of that conjecture for the flag manifold and present massive experimentation (over 12 GigaHertz-Years) that supports our refined conjecture. We also establish relationships between different cases of the conjecture and describe some new phenomena uncovered in this experimentation.

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James Ruffo, Yuval Sivan, Evgenia Soprunova, Frank Sottile. 2005-02-02. Experimentation and conjectures in the real Schubert calculus for flag manifolds (extended abstract). https://arxiv.org/abs/math/0502040

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