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.)