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Totally nonnegative Grassmannian and Grassmann polytopes

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arxiv 1506.00603 v1 pith:SX3UUZGI submitted 2015-06-01 math.CO hep-thmath.AGmath.RT

Thomas Lam This is my paper · ORCID
classification math.COhep-thmath.AGmath.RT
keywords articlegivegrassmanngrassmannianhalflecturenonnegativepolytopes
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These are lecture notes intended to supplement my second lecture at the Current Developments in Mathematics conference in 2014. In the first half of article, we give an introduction to the totally nonnegative Grassmannian together with a survey of some more recent work. In the second half of the article, we give a definition of a Grassmann polytope motivated by work of physicists on the amplituhedron. We propose to use Schubert calculus and canonical bases to replace linear algebra and convexity in the theory of polytopes.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Electrical networks and data analysis in phylogenetics

    math.CO 2024-12 conditional novelty 7.0 of 10

    A Kalmanson metric is an electrical resistance metric if and only if an explicitly constructed matrix lies in the totally nonnegative Isotropic Grassmannian with a nonvanishing Plücker coordinate.

  2. Points on Rational Normal Curves and the ABCT Variety

    math.AG 2024-12 conditional novelty 6.0 of 10

    The paper derives a recursive formula for the cohomology class of the ABCT variety V(3,n) inside the Grassmannian G(3,n), using a determinantal realization and Porteous' formula, and matches special coefficients to Eu...

  3. Brave new categorical spectral positive Schubert geometry and the categorical Dual Amplituhedron

    math.CT 2026-06 unverdicted novelty 5.0 of 10

    The dissertation rewrites positive Schubert geometry via spectral algebraic geometry and differential cohesion to construct a categorical dual to the Amplituhedron with a De Rham volume.

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