Incidence geometry of the totally nonnegative Grassmannian

The totally nonnegative Grassmannian parametrizes vector spaces with non-negative Plücker coordinates. In this talk, I will introduce the positive incidence locus, the set of vector spaces contained in a larger-dimensional totally nonnegative vector spaces. I will describe the positive incidence locus through its positroid coverings in the cases Gr(2, n) and Gr(3, 6), Gr(3, 7) and Gr(3, 8). In larger Grassmannians, I will explain the new phenomena that arise and the structure of the algebraic boundaries. Based on joint work with Ran Tessler and with Thomas Lam and Jianrong Li.