A twistor approach to conformal higher spin theory

In this talk we will discuss the twistor formulation of Conformal Higher Spin theory in four dimensions and construct a twistor space action which generalises the well known actions for Yang-Mills and Conformal Gravity. We will discuss the use of the twistor action for efficiently computing scattering amplitudes and discuss the restriction to a ghost free unitary theory. Finally we discuss the use of twistor methods to construct conserved charges for the linearised and asymptotically flat limits of the theory.