Cluster algebras and tilings of amplituhedra

Physicists Arkani-Hamed and Trnka introduced the amplituhedron to better understand scattering amplitudes in N=4 super Yang-Mills theory. The amplituhedron is the image of the totally nonnegative Grassmannian under the "amplituhedron map". Examples of amplituhedra include cyclic polytopes, the totally nonnegative Grassmannian itself, and cyclic hyperplane arrangements. Of primary interest to physics are tilings of amplituhedra, which are roughly analogous to subdivisions of polytopes. This talk is a follow-up to Matteo's talk on BCFW tilings of m=4 amplituhedra. I will focus on the surprising connection between tilings of m=4 amplituhedra and the cluster algebra structure of the Grassmannian. No knowledge of cluster algebras will be assumed. All results mentioned in this talk are joint work with Even-Zohar, Lakrec, Parisi, Tessler and Williams.