2015/06/01 by Thomas Lam, Lam, Thomas · 3 citations
Materials Science · Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematics and Applications #Polymer Nanocomposites and Properties #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1506.00603
openalex publication_date 2015/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.