Kick-Off meeting 13-17 January 2025: webpage and seminars

Midterm meeting 18-22 May 2026: webpage

Artificial intelligence for High Energy Physics - EPFL 10-20 June 2025 .

Non perturbative aspects of quantum field theories - UCM 18-21 June 2025 .

• Luciano Loris Viteritti:

Introduction to Jax, Automatic Differentiation, Flax and all that (I)

Introduction to Jax, Automatic Differentiation, Flax and all that (II)

Variational Monte Carlo methods with Neural Networks

• Zakari Denis:

Simulating lattice Fermions with Neural Networks

Bosons in 3D Harmonic Trap with Neural Networks

• Jamie Taylor: An Introduction to Solving PDEs Using Neural Networks

Abstract: In recent years, advances in machine learning techniques have begun to make their way into numerical analysis, offering new toolkits for tackling problems arising from partial differential equations (PDEs), with a wealth of new capabilities - and limitations - compared to more classical methods. Whilst many new ideas have been proposed for integrating neural networks (NNs) with PDE methods, the aim of this course is to consider simple test cases to introduce attendees to key concepts underlying such methodologies. In particular, we will focus on the most established methodology: Physics-Informed Neural Networks (PINNs). The three cornerstones of any such implementation are the choice of an appropriate loss function to be minimized, the NN architecture, and the optimization strategy employed, which will be the focus of this course. The course aims to be as self-contained as possible, however, familiarity with classical methods (e.g. FEM) and elementary concepts from data science-based machine learning (e.g. simple NNs, stochastic gradient descent) will be beneficial.

• Lorenzo Di Pietro: A Bootstrap Study of Confinement in AdS

Abstract: I will discuss the confinement problem for gauge theories in rigid AdS background, and its formulation in terms of boundary conditions, focussing on pure Yang-Mills theory and QCD with fundamental matter. In this formulation an important role is played by the conformal correlators at the boundary of AdS. The Dirichlet boundary condition for the gauge field is conjectured to disappear via merger and annihilation, as signaled by the lightest scalar singlet operator approaching marginality as the coupling increases. I will explain how to test this and similar scenarios (higgsing and decoupling) using both perturbative calculations and non-perturbative constraints from the numerical conformal bootstrap. 

• Andrea Guerrieri: S-Matrix Bootstrap

Abstract: In these lectures I will give an overview of the non-perturbative S-matrix bootstrap program.  First I will focus on gapped systems, discussing basic concepts, such as dispersion relations and unitarity constraints, and explaining what we can learn by asking bootstrap questions.  Then I will consider gapless scattering, such as goldstones and gravitons, and explain how unitarity constraints relax into positivity bounds and how the two are connected to each other. As a part of these lectures I will review what news we have learned about experimental data, and strongly coupled theories, from Analyticity, Crossing, and Unitarity.

• Xinan Zhou: Giant Graviton Correlators as Defect Systems

Abstract: In this talk, I will discuss correlation functions in 4d N = 4 SYM involving two maximal giant gravitons and two light 1/2-BPS operators. I will argue that it is most natural to view them as two-point correlators in the presence of a zero dimensional defect. Using this picture together with analytic bootstrap techniques, I will show how all infinitely many such correlators can be fully fixed just from symmetries and consistency conditions. Moreover, I will point out a hidden higher dimensional symmetry which repackages these correlators into a simple generating function. I will also present evidence that the same symmetry holds at weak coupling for loop correction integrands.

• Matthias Wilhelm: Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning

Abstract: In this talk, we will present recent progress on applying machine-learning techniques to improve calculations in theoretical physics, in which we desire exact and analytic results. One example are so-called integration-by-parts reductions of Feynman integrals, which pose a frequent bottleneck in state-of-the-art calculations in theoretical particle and gravitational-wave physics. These reductions rely on heuristic approaches for selecting a finite set of linear equations to solve, and the quality of the heuristics heavily influences the performance. In this talk, we investigate the use of machine-learning techniques to find improved heuristics. We use funsearch, a genetic programming variant based on code generation by a Large Language Model, in order to explore possible approaches, then use strongly typed genetic programming to zero in on useful solutions. Both approaches manage to re-discover the state-of-the-art heuristics recently incorporated into integration-by-parts solvers, and in one example find a small advance on this state of the art.

• Bo Wang: Kaluza-Klein AdS Virasoro-Shapiro and Veneziano Amplitudes

Abstract: I will report recent progress on the AdS Virasoro-Shapiro amplitude and the AdS Veneziano amplitude for half-BPS operators with arbitrary Kaluza-Klein modes. The key is a novel formalism built out as a bootstrap approach directly in the world-sheet representation. This approach yields a structural string description of AdS amplitude and a precise correspondence with correlators in N=4 SYM: at the first order in the curvature corrections we obtain a unique solution. I will also discuss the applications to broader holographic models beyond AdS5xS5.

• Eduardo García-Valdecasas: Entanglement asymmetry and spontaneously broken symmetries

Abstract: Entanglement asymmetry is a relative entropy that faithfully measures the breaking of a symmetry in a subregion. We explore some applications in theories with spontaneously broken higher form symmetries. We will start with discrete abelian symmetries and then discuss continuous symmetries. We will be able to recover the Mermin-Wagner-Coleman theorem and refine it for the case of subregions.