For zoom link please email s.nagyATqmul.ac.uk There will be a pre-seminar for students at 13:30. Abstract: I will discuss 2 recent results arising out of the recent resurgence in concrete tests / predictions of AdS/CFT over the last few years. The first is the precise identification of the CFT operators dual to single particle supergravity states (based on 2007.095395) and the second is a forthcoming work explicitly relating four-point correlators to a string effective action on AdSxS.

We will show how to obtain half-BPS four-point correlation functions in N=4 SYM at up to 3 loops using symmetries, analytic properties the Wilson loop/correlator duality, planarity and some minimal knowledge of the OPE structure relating four-point correlators of different charges. These can be used to verify recent predictions for OPE coefficients arising from integrability.

Abstract: There has been much progress in understanding the four-point correlator of Stress Energy multiplets in N=4 SYM recently. I will discuss recent progress in evaluating high loop Feynman integrals using leading singularities, asymptotics and the symbol. This is used to evaluate the three-loop four-point correlation function from its integrand. Then I will show how the full (parity even and odd) 5-point amplitude can be found from the same four-point correlator integrand.

I will review weak-weak dualities relating scattering amplitudes to Wilson loops on the one hand and correlation functions of gauge invariant operators on the other. The Wilson loop / amplitude duality has lead to both numerical and analytic results for MHV scattering amplitudes at two-loops and beyond, including the determination of two loop MHV n-point scattering amplitudes for any n in a certain kinematical regime. The duality with correlation functions has been extended to all scattering amplitudes in the theory and we give explicit examples illustrating this.

We introduce the Wilson loop/amplitude duality, which states that certain gluon amplitudes in N=4 SYM are equivalent to light-like polygonal Wilson loops. We will illustrate the duality's power by computing the one loop Wilson loop analytically (matching with the known amplitudes) and then the two loop Wilson loop numerically for any number of edges. If the duality continues to hold we can thus compute two loop MHV amplitudes for any number of incoming particles. In the second part of the talk we discuss the recently conjectured new symmetry dual superconformal symmetry of the complete S-matrix of N=4 SYM. We prove its presence at tree-level and find new constraints it puts on the one loop amplitude.