The "positroid stratification" of the Grassmannian of k-planes in n-space, studied by Lusztig, Postnikov, and many others, stands in between the (beautiful) Bruhat decomposition and the (unspeakably awful) matroid decomposition. Rather than being indexed by partitions or by (representable) matroids, its strata are indexed by bounded juggling patterns.

IA'll explain how this stratification naturally arises from (1) Poisson geometry, (2) characteristic p geometry, or (3) nonnegative real geometry. For good measure, IA'll connect it to the affine flag manifold (where one sees unbounded juggling patterns), and if time permits, to the physics of scattering amplitudes in certain quantum field theories. This work is joint with Thomas Lam and David Speyer.