From Quantum Field Theory to Quantum Gravity and the Sachdev-Ye-Kitaev model

In the first part of this talk I will briefly introduce 0-dimensional Quantum Field Theory (QFT) and Matrix Models, which are known to be a succesfull discrete geometrical, QFT approach to 2D Quantum Gravity. I will then move on to Tensor Models, seen as natural QFT generalization of the celebrated Matrix Models. In the next part of the talk I will present the Sachdev-Ye-Kitaev model, which is known to be a toy model for holography, as well as the relations of this SYK model with various Tensor Models. Finally, I will present some recent results on these topics (various diagrammatic results but also the study of the effect of non-Gaussian average over the SYK random couplings).