Algebraic Geometry Working Seminar | Francisco Villacis | Principal Minors and Absolute Values

The classification of matrices by their principal minors has been an area of interest to many since at least the 1980s. In this talk we expand on this work by outlining a proof that, if two orthogonal projection matrices have the same principal minors, then the coordinatewise absolute value of their images coincide. Generalizing the ideas of the proof gives rise to a stratification of the Grassmannian which is coarser than the well-known matroid stratification of Gelfand-Goresky-MacPherson-Serganova. We conclude this talk with some applications of this theorem to geometry.

MC 5403