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My question is quite simple: what is the mathematical definition of the amplituhedron? … An older-sister MO question: The amplituhedron minus the physics Update: The paper The amplituhedron by Nima Arkani-Hamed and Jaroslav Trnka is now on the arxive. …

Is it possible to appreciate the geometric/polytopal properties of the amplituhedron without delving into the physics that gave rise to it? …

In the paper The Amplituhedron , Nima Arkani-Hamed and Jaroslav Trnka introduced the geometric object amplituhedron. It is defined as follows (see also the lecture notes). … The tree amplituhedron $\mathcal{A}_{n,k,m}$ is the image $\tilde{Z}(Gr_{k,n}^{\geq 0}) \subset Gr_{k,k+m}$. …

(The situation is reminiscent of "The amplituhedron minus the physics"...)       …

There have been many exciting dual representations of amplitudes including polytopes, twistor diagrams and the positive grassmannian leading to the concept of the amplituhedron, polylogs, multizeta …

See http://www.twistordiagrams.org.uk/papers/index.html for the description of historical developments that led to the discovery of amplituhedron. … Other useful information can be found at http://ncatlab.org/nlab/show/amplituhedron …

He also briefly referred to the amplituhedron. … Video1, Video2, Video3, Video4 Postnikov's ten minutes explanation of the amplituhedron starts here. …

The construction of the amplituhedron $P_{n,k,m}$ is summarized on page 23. … This space is called the amplituhedron. …

He also briefly referred to the amplituhedron. … Video1, Video2, Video3, Video4 Postnikov's ten minutes explanation of the amplituhedron starts here. …

, in which the amplituhedron is Zariski-dense). … The principal job of the amplituhedron is to help nail down this form: the form is required to be well-defined on the interior of the amplituhedron. …

There’s a simpler (and older) Amplituhedron-like object called the associahedron that can be thought of as what the Amplituhedron looks like on the surface of a string, and CHY’s setup can be thought of … as a sophisticated map that takes this object and turns it into the Amplituhedron." …

What are the roles that the classic number arrays-- Eulerian, Narayana--play in the application of totally non-negative Grassmannians, or amplituhedrons, to string / twistor scattering theory? (This …

Goncharov, Alexander Postnikov, and Jaroslav Trnka (arXiv:1212.5605 [hep-th]), coauthor Arkani-Hamed asserted the following research objective in an associated lecture The Amplituhedron: We can't just … class of non-Hilbert dynamical systems in which unitarity and locality are encoded emergently, in geometric objects called amplituhedrons — for details see Gil Kalai's MathOverflow question "What is the amplituhedron …

On the other hand, Lukowski, Parisi, and Williams assert on p. 35 of "The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron" that the f-vectors of $Trop^+$ $Gr_{2,n}$ are those …

Nima Arkani-Hamed, Yuntao Bai, Song He, and Gongwang Yan: The search for a theory of the S-Matrix has revealed surprising geometric structures underlying amplitudes ranging from the worldsheet to the amplituhedron …