# The positive Grassmannian, the amplituhedron, and cluster algebras

@inproceedings{Williams2021ThePG, title={The positive Grassmannian, the amplituhedron, and cluster algebras}, author={Lauren K. Williams}, year={2021} }

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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