Manolis Tsakiris: Results on the algebraic matroid of the determinantal variety

Abstract.

This talk will report progress on the characterization of the algebraic matroid of the classical determinantal variety; a problem related to low-rank matrix completion. A family of base sets of the matroid is presented, which characterizes the entire matroid in special cases. The proof relies on the integration of a notion of relaxed supports of linkage matching fields, an interpretation of the problem of bounded-rank matrix completion as a linear section problem on the Grassmannian, and a class of local coordinates on the Grassmannian described by Sturmfels and Zelevinsky in 1993.