In this talk I will discuss how to compute amplitudes on AdS, using the analytic conformal bootstrap and the AdS/CFT correspondence. I will also discuss how to include higher trace operators in a simplified setup.

I will discuss how to constrain four-point correlators involving at least one quarter BPS operator in N=4 Super Yang-Mills. I will present what can be learned by using crossing symmetry, chiral algebra, superspace techniques, and the structure of the operator product expansion. Finally, I will show how to make contact with the superconformal bootstrap program. Contact your local Triangle organiser or Bogdan Stefanski for Zoom link.

In this talk I will discuss how to extract the most trascendental piece of the four graviton amplitude in type IIB supergravity on AdS_5 \times S_5 at any loop order, from the dual four point function in N=4 Super Yang Mills. I will describe how to construct this part of the correlator/amplitude and its significance. I will conclude with some open problems and future directions. [Please email alejandro.cabo_bizet@kcl.ac.uk for the Zoom link]

TBA