Maximum likelihood duality for determinantal varieties

In the preprint arXiv:1210.0198 Hauenstein, Rodriguez, 
and Sturmfels discovered a conjectural bijection between 
critical points of the likelihood function on the complex 
manifold of matrices of rank r and cricital points on the 
complex manifold of matrices of co-rank r-1. I'll discuss 
a proof of that conjecture for rectangular matrices and
symmetric matrices. (Joint work with Jose Rodriguez.)