We will discuss a connection between OPE algebras appearing in celestial holography for various theories and the `colour-kinematics duality' in the bulk spacetime description of those theories. Both the celestial algebras and the colour-kinematics duality take a particularly simple form for self-dual Yang-Mills and gravity. In particular, we show that the $Lw_{1+\infty}$ celestial algebra recently unveiled in self-dual gravity arises from the soft expansion of an area-preserving diffeomorphism algebra, which plays the role of the kinematic algebra in the colour-kinematics duality. We also present deformations of the celestial algebras resulting from Moyal deformations of the self-dual theories, e.g. the deformation of $Lw_{1+\infty}$ into $LW_{1+\infty}$ in the case of self-dual gravity. In addition, we discuss the relation of these deformations to higher-spin theories of massless particles that can be thought of as extensions of self-dual Yang-Mills and gravity. Finally, we present a proof that tree-level scattering amplitudes in the theories we focus on vanish, signalling their classical integrability, which is an S-matrix version of the Ward conjecture for integrable systems.

I will give an introduction to current topics in the study of scattering amplitudes of gauge theory and gravity. There will be four two-hour lectures, and the plan is as follows. Lecture 1 will review basic modern techniques for scattering amplitudes, including recursion relations. Lecture 2 will present an overview of the relations describing gravity as a double copy of gauge theory, both for scattering amplitudes and for solutions to the equations of motion. Lecture 3 will introduce the formalism of the scattering equations, leading to the CHY formulas for amplitudes in theories of massless particles. Lecture 4 will present new developments in computing field-theory amplitudes from string-theory-inspired techniques, via a new type of worldsheet model known as ambitwistor string. This leads to an extension of the scattering equations to loop level.

I will give an introduction to current topics in the study of scattering amplitudes of gauge theory and gravity. There will be four two-hour lectures, and the plan is as follows. Lecture 1 will review basic modern techniques for scattering amplitudes, including recursion relations. Lecture 2 will present an overview of the relations describing gravity as a double copy of gauge theory, both for scattering amplitudes and for solutions to the equations of motion. Lecture 3 will introduce the formalism of the scattering equations, leading to the CHY formulas for amplitudes in theories of massless particles. Lecture 4 will present new developments in computing field-theory amplitudes from string-theory-inspired techniques, via a new type of worldsheet model known as ambitwistor string. This leads to an extension of the scattering equations to loop level.

I will give an introduction to current topics in the study of scattering amplitudes of gauge theory and gravity. There will be four two-hour lectures, and the plan is as follows. Lecture 1 will review basic modern techniques for scattering amplitudes, including recursion relations. Lecture 2 will present an overview of the relations describing gravity as a double copy of gauge theory, both for scattering amplitudes and for solutions to the equations of motion. Lecture 3 will introduce the formalism of the scattering equations, leading to the CHY formulas for amplitudes in theories of massless particles. Lecture 4 will present new developments in computing field-theory amplitudes from string-theory-inspired techniques, via a new type of worldsheet model known as ambitwistor string. This leads to an extension of the scattering equations to loop level.

I will give an introduction to current topics in the study of scattering amplitudes of gauge theory and gravity. There will be four two-hour lectures, and the plan is as follows: Lecture 1 will review basic modern techniques for scattering amplitudes, including recursion relations. Lecture 2 will present an overview of the relations describing gravity as a double copy of gauge theory, both for scattering amplitudes and for solutions to the equations of motion. Lecture 3 will introduce the formalism of the scattering equations, leading to the CHY formulas for amplitudes in theories of massless particles. Lecture 4 will present new developments in computing field-theory amplitudes from string-theory-inspired techniques, via a new type of worldsheet model known as ambitwistor string. This leads to an extension of the scattering equations to loop level.

We will discuss the relation between perturbative gauge theory and perturbative gravity, and look at how this relation extends to some exact classical solutions. First, we will review the double copy prescription that takes gauge theory amplitudes into gravity amplitudes, which has been crucial to progress in perturbative studies of supergravity. Then, we will see that the self-dual sectors provide an important insight into the relation between the theories. A key role is played by a kinematic algebraic structure mirroring the colour structure. Finally, we will see how these ideas extend to some exact classical solutions, namely black holes and plane waves. This leads to a relation of the type Schwarzschild as Coulomb charge squared.