In this talk I will review the work that has been done by me, N. Gromov, V. Kazakov, G. Korchemsky and G. Sizov on the analysis of fishnet Feynman graphs in a particular scaling limit of $\mathcal N=4$ SYM, a theory dubbed $\chi$FT$_4$. After introducing said theory, in which the Feynman graphs take a very simple fishnet form — in the planar limit — I will review how to exploit integrable techniques to compute these graphs and, consequently, extract the anomalous dimensions of a simple class of operators.

I will lead an informal discussion centered on discrete data that need to be specified when reducing 6d relative theories on an internal manifold M and how they determine symmetries of the resulting theory T[M].

Mean field games (MFG) and mean field control problems (MFC) are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative situations with a large finite number of agents. They have found a broad range of applications, from economics to crowd motion, energy production and risk management. Scalable numerical methods are a key step towards concrete applications. In this talk, we propose several numerical methods for MFG and MFC. These methods are based on machine learning tools such as function approximation via neural networks and stochastic optimization. We provide numerical results and we investigate the numerical analysis of these methods by proving bounds on the approximation scheme. If time permits, we will also discuss model-free methods based on extensions of the traditional reinforcement learning setting to the mean-field regime.