Unwinding The Amplituhedron

Arkani-Hamed and Trnka recently defined an object, which they dubbed the amplituhedron, which encodes the scattering amplitudes for planar N=4 super Yang-Mills.  This object feels polytopal, and indeed, in simple examples, it is a cyclic polytope inside projective space.  However, in general, it lives in a Grassmannian rather than in a projective space.  Amplituhedra are closely linked to the geometry of total positivity; indeed, the totally non-negative part of a Grassmannian is also an example of an amplituhedron.  I will try to explain some of what this means, and report on joint work with Arkani-Hamed and Trnka in which we give a new and simpler definition of the amplituhedron

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