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Presented By: Learning Seminar in Algebraic Combinatorics - Department of Mathematics

Learning Seminar in Algebraic Combinatorics -- The Totally Nonnegative Grassmannian as a Positive Geometry

Amanda Schwartz

The Grassmannian Gr(k,n) has a stratification into positroid varieties which can be indexed by many objects including move-equivalence classes of reduced plabic graphs and bounded affine permutations. Given a bounded affine permutation f, the positroid variety $\Pi_f$ and the corresponding positroid cell $\Pi_{f,\geq 0}$ in the TNN Grassmannian form a positive geometry $(\Pi_f, \Pi_{f,\geq 0})$. We will see how to compute the canonical form of a positroid variety using a reduced plabic graph corresponding to that variety.

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