• Corpus ID: 239050279

The positive Grassmannian, the amplituhedron, and cluster algebras

  title={The positive Grassmannian, the amplituhedron, and cluster algebras},
  author={Lauren K. Williams},
  • L. Williams
  • Published 21 October 2021
  • Mathematics, Physics
The positive Grassmannian Gr k,n is the subset of the real Grassmannian where all Plücker coordinates are nonnegative. It has a beautiful combinatorial structure as well as connections to statistical physics, integrable systems, and scattering amplitudes. The amplituhedron An,k,m(Z) is the image of the positive Grassmannian Gr ≥0 k,n under a positive linear map R → R. We will explain how ideas from oriented matroids, tropical geometry, and cluster algebras shed light on the structure of the… 
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