Abstract:
Positroids are combinatorial objects that can be used to index the different strata in certain well-behaved decompositions of the Grassmannian and its positive part. In this talk I will present joint work with Federico Ardila and Lauren Williams, in which we study some of the combinatorial properties of positroids. As an application, we prove da Silva's 1987 conjecture that any positively oriented matroid is representable over the field of rational numbers. In particular, this implies that the positive matroid Grassmannian (or positive MacPhersonian) is homeomorphic to a closed ball.