Tilings and cluster algebras for the amplituhedron

Recent years have seen the discovery of many intriguing connections between algebraic combinatorics and theoretical particle physics, specifically in scattering amplitudes. One such connection is the amplituhedron (Arkani-Hamed--Trnka 2013), a generalization of the nonnegative Grassmannian which admits a related combinatorial and geometric structure. Its "volume'' expresses scattering amplitudes in certain quantum field theories. Another such connection is the appearance of combinatorial cluster-algebraic structures in scattering amplitudes (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.