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Formulating a Schubert problem as the solutions to a system of equations in either Plucker space or in the local coordinates of a Schubert cell usually involves more equations than variables. Using reduction to the diagonal, we previously gave a primal-dual formulation for Schubert problems that involved the same number of variables as equations (a square formulation). Here, we give a different square formulation by lifting incidence conditions which typically involves fewer equations and variables. Our motivation is certification of numerical computation using Smales alpha-theory.
In the recent paper [arXiv:1612.06893] P. Burgisser and A. Lerario introduced a geometric framework for a probabilistic study of real Schubert Problems. They denoted by $delta_{k,n}$ the average number of projective $k$-planes in $mathbb{R}textrm{P}^
Many aspects of Schubert calculus are easily modeled on a computer. This enables large-scale experimentation to investigate subtle and ill-understood phenomena in the Schubert calculus. A well-known web of conjectures and results in the real Schubert
The Macaulay2 package NumericalSchubertCalculus provides methods for the numerical computation of Schubert problems on Grassmannians. It implements both the Pieri homotopy algorithm and the Littlewood-Richardson homotopy algorithm. Each algorithm has
We show a Z^2-filtered algebraic structure and a quantum to classical principle on the torus-equivariant quantum cohomology of a complete flag variety of general Lie type, generalizing earlier works of Leung and the second author. We also provide var
We describe a new approach to the Schubert calculus on complete flag varieties using the volume polynomial associated with Gelfand-Zetlin polytopes. This approach allows us to compute the intersection products of Schubert cycles by intersecting faces of a polytope.