The amplituhedron (Arkani Hamed-Trnka 2013) is a semialgebraic subset of the Grassmannian admitting a natural logarithmic form conjectured to express scattering amplitudes in N = 4 super Yang–Mills theory. It has a geometric and combinatorial structure originating in the nonnegative Grassmannian. It was recently realized that in many quantum field theories, scattering amplitudes contain cluster algebraic expressions (starting with Golden-Goncharov-Spradlin-Vergu-Volovich 2013). In this talk I will introduce these topics and discuss how they are connected and clarified using the recursion relations for scattering amplitudes introduced by Britto, Cachazo, Feng and Witten (BCFW 2005).
Based on joint works with Even-Zohar, Parisi, Sherman-Bennett, Tessler and Williams.