Defining equations of orbit closures in skew symmetric tensors

Defining equations for varieties in spaces of tensors are useful for applications such as algebraic statistics and signal processing. In the case of skew symmetric tensors, the varieties we study are the Grassmannian, its secant and tangential varieties, and their singular loci. These varieties can be described as closures orbits under the action of the general linear group. With Giorgio Ottaviani, we have started with the classical technique of the symbolic method and the work initiated by G.C. Rota and coauthors. We work to understand the equations defining these orbit closures in terms of special fillings of Young tableau. We are naturally lead to study paths in the related Young lattice.