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

Mathematics – Algebraic Geometry

Scientific paper

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Extended abstract, 12 pages, 4 .eps figures

Scientific paper

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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