Lower bounds for numbers of real solutions in problems of Schubert calculus

@article{Mukhin2014LowerBF,
  title={Lower bounds for numbers of real solutions in problems of Schubert calculus},
  author={Evgeny Mukhin and Vitaly O. Tarasov},
  journal={Acta Mathematica},
  year={2014},
  volume={217},
  pages={177-193}
}
We give lower bounds for the numbers of real solutions in problems appearing in Schubert calculus in the Grassmannian $${\mathop{\rm Gr}(n,d)}$$Gr(n,d) related to osculating flags. It is known that such solutions are related to Bethe vectors in the Gaudin model associated to $${\mathop{\rm gl}_n}$$gln. The Gaudin Hamiltonians are self-adjoint with respect to a non-degenerate indefinite Hermitian form. Our bound comes from the computation of the signature of that form. 
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