The $m=1$ Amplituhedron and Cyclic Hyperplane Arrangements

DOI10.1093/imrn/rnx140zbMath1429.52024OpenAlexW3104493577MaRDI QIDQ5243327

Steven N. Karp, Lauren K. Williams

Publication date: 18 November 2019

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imrn/rnx140

zbMATH Keywords

(tree) amplituhedroncyclic hyperplane arrangement

Mathematics Subject Classification ID

Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) (51M35)

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Shelling the \(m=1\) amplituhedron ⋮ Grass(mannian) trees and forests: Variations of the exponential formula, with applications to the momentum amplituhedron ⋮ Decompositions of amplituhedra ⋮ Boundaries of the amplituhedron with \texttt{amplituhedronBoundaries} ⋮ The 𝑚=2 amplituhedron and the hypersimplex: Signs, clusters, tilings, Eulerian numbers ⋮ The ABJM Amplituhedron ⋮ The amplituhedron crossing and winding numbers ⋮ Strands algebras and the affine highest weight property for equivariant hypertoric categories ⋮ Interview with Lauren K. Williams ⋮ The \(m=2\) amplituhedron and the hypersimplex ⋮ Regularity theorem for totally nonnegative flag varieties ⋮ The positive Grassmannian, the amplituhedron, and cluster algebras ⋮ Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties ⋮ Boundary measurement and sign variation in real projective space ⋮ A study in \(\mathbb{G}_{\mathbb{R} , \geq 0} ( 2 , 6 )\): from the geometric case book of Wilson loop diagrams and SYM \(N =4\) ⋮ Non-planar BCFW Grassmannian geometries ⋮ From momentum amplituhedron boundaries to amplitude singularities and back ⋮ Triangulations and canonical forms of amplituhedra: a fiber-based approach beyond polytopes ⋮ Parity duality for the amplituhedron ⋮ Positive geometry, local triangulations, and the dual of the amplituhedron ⋮ Towards the gravituhedron: new expressions for NMHV gravity amplitudes ⋮ The totally nonnegative Grassmannian is a ball ⋮ THE COMBINATORICS OF TENSOR PRODUCTS OF HIGHER AUSLANDER ALGEBRAS OF TYPEA ⋮ Amplituhedra, and beyond

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