Positroid varieties I: juggling and geometry

Understand

While the intersection of the Grassmannian Bruhat decompositions for all coordinate flags is an intractable mess, the intersection of only the {\em cyclic shifts} of one Bruhat decomposition turns out to have many of the good properties of the Bruhat and Richardson decompositions.

• This decomposition coincides with the projection of the Richardson stratification of the flag manifold, studied by Lusztig, Rietsch, and Brown-Goodearl-Yakimov.
• However, its cyclic-invariance is hidden in this description.
• Postnikov gave many cyclic-invariant ways to index the strata, and we give a new one, by a subset of the affine Weyl group we call {\em bounded juggling patterns}.