Cluster structures on spinor helicity and momentum twistor varieties

We study cluster structures on spinor helicity and momentum twistor varieties which describe the kinematic spaces of massless scattering with and without dual conformal symmetry. Both are instances of partial flag varieties. We exhibit embeddings of the corresponding cluster algebras into cluster algebras of sufficiently large Grassmannians and show how the former is obtained by specializing and freezing certain cluster variables from the latter. This is work in progress with Jianrong Li.