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 scatterings in physics. Both varieties are certain 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 freezing certain cluster variables from the latter. This is joint work with Lara Bossinger.