David Speyer, Massachusetts Institute of Technology

Positroid Varieties -- a Beautiful Stratification of the Grassmannian

George Lusztig and Alex Postnikov have studied those points on the Grassmannian all of whose Pl"ucker coordinates are nonnegative, and found that they can be grouped into strata indexed by combinatorial objects called positroids. We follow these positroids into the rest of the Grassmannian and find that their Zariski closures form an elegant stratification which refines the classical stratification into Schubert cells. In particular, the strata are Cohen-Macaulay and normal, are defined by explicit equations and have explicit Grobner degenerations. Studying the cohomology classes of these varieties gives geometrical meaning to Stanley's symmetric functions and Postnikov's toric Schur functions.

I come at this material from an algebraic geometry background, but most of what I say should be quite understandable to combinatorialists, Lie theorists or geometers of all sorts.

Joint work with Allen Knutson and Thomas Lam.

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