In this lecture, we will examine the relationship between quantum field theory and discrete lattice models. In particular, we will discuss this link in the context of critical phenomena, connecting statistical lattice systems at criticality with conformal field theories.

We will focus on exactly solvable two-dimensional statistical lattice models—such as the Restricted Solid-on-Solid (RSOS) model—and explore how their continuum limits can be obtained using integrability-based techniques.

Sascha Gehrmann’s (University of Oxford) research centers on the theoretical analysis of one-dimensional lattice systems, with a particular focus on critical behavior, effective field theories, and integrability. His work utilizes analytical frameworks, including Bethe Ansatz methods and the ODE/IQFT correspondence, to explore the structural properties of exactly solvable models and their continuum limits. He received his PhD in 2024 from the Leibniz University of Hannover and is currently a Postdoctoral Researcher at Oxford.

In these lectures, we will explore symmetries from the point of view of topological defects, focusing on non-invertible symmetries in 2d quantum field theories. We will discuss the mathematical structure underlying these symmetries, namely the fusion category formed by topological line defects. We will show how gauging and duality defects work, and introduce the symmetry topological field theory (SymTFT) as a useful organizing framework. Finally, we will look at concrete examples from rational conformal field theories and discuss some dynamical implications of these symmetries.

Lea Bottini is a theoretical physicist working on generalized and non-invertible symmetries in quantum field theory. She is currently a postdoctoral researcher at IHES in Paris. She obtained her DPhil from the Mathematical Institute at the University of Oxford, and her master’s degree from the University of Milano-Bicocca in Italy.

We will introduce the essentials of the Thermodynamic Bethe Ansatz (TBA), starting from the basic structure of Bethe-ansatz–solvable models and the emergence of integral equations in the thermodynamic limit. We will discuss how the TBA framework captures both the UV and IR behaviour of integrable quantum field theories, and how it naturally connects to conformal field theory, allowing one to extract quantities such as effective central charges. The course will also include practical sessions, where we work through explicit examples and simple numerical implementations to see the TBA in action.

Alessio Miscioscia works on quantum field theories in various dimensions, with a focus on thermal aspects of conformal field theories and on RG flows among both unitary and non-unitary models. He obtained his PhD from the University of Hamburg and DESY in 2025 and, in the same year, joined a postdoctoral position at  the C.N. Yang Institute for Theoretical Physics at Stony Brook University.