Combinatorics and Optimization Graduate Student Colloquium

Title: Basis Shape Loci and the Positive Grassmannian

Abstract: We study the set of k-dimensional planes in R^n admitting a basis of vectors with prescribed supports. We describe conditions on the prescribed support shape for when this set of planes has the expected dimension in the Grassmannian, and for when this set of planes intersects the positive Grassmannian in its full dimension.