K polynomials and matroids

Our motivation comes from the well known fact that a wedge (exterior product) of vectors is zero if and only if the vectors involved are linearly dependent. We generalize this to vanishing of symmetrized tensors which has a surprising connection to matroids and a variety which we call a matrix orbit closure. This is the closure of those matrices obtained from a fixed matrix M by performing row operations and column scalings to M. I will present an explicit combinatorial formula for the K-polynomial of a matrix orbit closure and discuss some interesting combinatorial problems the formula gives rise to. This is joint work with Alex Fink.