Based on Ravi Vakil's geometric proof of the Littlewood-Richardson rule, we developed a numerical homotopy continuation algorithm for finding all solutions to Schubert problems on Grassmannians. For generic Schubert problems the number of paths tracked is optimal. The Littlewood-Richardson homotopy algorithm is implemented using the path trackers of the software package PHCpack. This is joint work with Frank Sottile and Ravi Vakil.
SIAM Conference on Algebraic Geometry, Minisymposium on Applications of Numerical Algebraic Geometry, Raleigh, 6-9 October 2011.