Mukhin, EvgenyTarasov, Vitaly2017-11-092017-11-092016-09Mukhin, E., & Tarasov, V. (2016). Lower bounds for numbers of real solutions in problems of Schubert calculus. Acta Mathematica, 217(1), 177–193. https://doi.org/10.1007/s11511-016-0143-3https://hdl.handle.net/1805/14484We give lower bounds for the numbers of real solutions in problems appearing in Schubert calculus in the Grassmannian 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 glngln. 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.enPublisher PolicySchubert calculusreal solutionslower boundsArticle