A brief description of the four mini-courses:

- Bootstrapping two-dimensional loop models by Sylvain Ribault - IPhT, Saclay

Description: In two-dimensional conformal field theory, analytic bootstrap methods have led to exact solutions of minimal models and Liouville theory. However, analytic methods fall short of being able to solve loop models -- a class of CFTs that include percolation and the O(N) model. I will review how progress is made by combining analytic methods with numerical bootstrap methods. In the absence of unitarity, these numerical methods rely on the exact knowledge of the spectrum for determining structure constants. In the picture that emerges, correlation functions in loop models are characterized by combinatorial maps, while global symmetries such as O(N) do not play a fundamental role.

The gravitational S-matrix by Alexander Zhiboedov - CERN

Description: We review the basic properties of gravitational scattering. We discuss to what extent they are compatible with the principles of S-matrix theory.

- Topics on QFT in AdS by Shota Komatsu - CERN

Description: I will discuss several topics related to QFT in AdS, emphasizing its potential use in analyzing the strongly coupled dynamics of QFT. In the first lecture, I will discuss the flat-space limit of AdS; how the conformal correlators become flat space amplitudes and what are subtleties in taking the flat-space limit. In the second lecture, I will discuss the application to theories with dynamically generated mass gap, emphasizing connections to conformal bootstrap. In the third lecture, I will discuss the interplay between the flat-space limit of AdS and non-invertible symmetry.

- The algebraic approach: when, how, and why? by Jonathan Sorce - MIT

Description: The goal of this mini-course is to explain the merits of algebraic quantum field theory to a broad audience. We will explore (i) how to know when a particular question calls for an algebraic answer, (ii) how to apply the tools of algebraic QFT to such a problem, and (iii) why quantum field theorists of all stripes stand to benefit from a basic knowledge of algebraic quantum fields. The first lecture will focus on the big-picture motivation behind the algebraic approach to quantum field theory, and an elaboration of its basic tools. Subsequent lectures will explain some of the modern achievements of the algebraic toolkit, including a proof of the averaged null energy condition and an enhanced understanding of black hole entropy. Relevant review articles include 1803.04993, 2302.01958, 2309.16766, but I will not assume any prior knowledge of algebraic quantum fields.