An amplituhedron is a positive geometry obtained as the image of a positive Grassmannian
under a linear transformation. In one standard
form, a positive 
-plane
represented by a matrix 
in 
and positive external data represented by a matrix 
in 
determine
 |
Here "positive external data" means that every ordered maximal 
minor of 
is positive. The image of 
under this map is the amplituhedron
. As part of its positive
geometry structure, it has a distinguished meromorphic differential
form called its canonical form. This form has
logarithmic singularities on the boundary,
with residues given by the corresponding forms of the
boundary pieces. For an amplituhedron, it encodes the
integrand of certain scattering
amplitudes in planar 
supersymmetric Yang-Mills
theory.
