Amplituhedron Geometry

I will review a surprising connection between the scattering of elementary particles in physics and the geometric object called amplituhedron, not known to mathematicians until relatively recently. It is a substantial generalization of the positive Grassmannians, studied in the last two decades in the context of plabic graphs and cluster algebras. The amplituhedron provides an excellent playground for new ideas in mathematics which have a direct impact on solving half-century old questions on all-loop order calculations in quantum field theory, but even more ambitiously can provide a path to a completely new mathematical framework for the description of fundamental laws of Nature.