The Amplituhedron and Positive Geometries

A tree amplituhedron is a geometric object generalizing the cyclic polytope and the positive Grassmannian. It was introduced by Arkani-Hamed and Trnka to give a geometric basis for the computation of scattering amplitudes in N=4 supersymmetric Yang-Mills theory. In particular, the physical computation of scattering amplitudes is reduced to finding the triangulations of the amplituhedron. I will start with a gentle overview of the amplituhedron. Then, I will explain how to find its triangulations in various cases. As amplituhedron is in the heart of the general theory of positive geometry, I will present some related examples of positive geometries arising in physics, as well. This is joint work with Leonid Monin and Matteo Parisi.