The Liouville equation has many applications: it describes surfaces of constant negative curvature and plays an important role in non-critical string theory. In this talk we discuss how to put the Liouville equation on the lattice in a completely integrable way; it will be possible to follow this talk online (please register at https://london-tqft.vercel.app)

In this talk, I will discuss how to compute the spectral curve of "segmented strings" in AdS_3. The motion of a string in this target space is integrable and the worldsheet theory can be discretized while preserving integrability. The corresponding embeddings are segmented strings, which generalize piecewise linear strings in flat space. I will present several examples. Next, I will introduce "brane tilings", which are doubly-periodic planar bipartite graphs. I will show that the motion of a closed segmented string can be embedded into the mutation dynamics of a certain brane tiling. This will enable us to compute the spectral curve by taking the determinant of the dressed adjacency matrix of the tiling. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

Lonti Autumn 2021 Series: Lecture 2. Live Tutorial. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. Abstract: In this lecture, we present a few elementary facts about Fermi surfaces, then discuss how to find interesting ``non-Fermi liquids'' via the AdS/CFT correspondence. We study different backgrounds (e.g. AdS, BTZ, and Reissner-Nordstrom), and the wave-equation of probe fields on top of these geometries. We discuss how to compute boundary two-point functions by solving the bulk equations and then explore the results.

Lonti Autumn 2021 Series: Lecture 2. Release of Recorded Lecture. Available at https://youtu.be/5IAx2ca_WU4 Abstract: In this lecture, we present a few elementary facts about Fermi surfaces, then discuss how to find interesting "non-Fermi liquids" via the AdS/CFT correspondence. We study different backgrounds (e.g. AdS, BTZ, and Reissner-Nordstrom), and the wave-equation of probe fields on top of these geometries. We discuss how to compute boundary two-point functions by solving the bulk equations and then explore the results.

The goal of this talk is twofold. Firstly, I would like to popularize the segmented string approach for solving the classical string dynamics on certain symmetric spacetimes where the string motion is integrable. This allows for an exact discretization which renders the equation of motion discrete in both space and time. The corresponding string solution is a segmented string. I will review the properties of segmented strings and relate them to discrete-time Toda-type lattices. The second goal of the talk is to understand a concrete setup: a (segmented) string hanging from the boundary of three-dimensional AdS spacetime. According to the gauge/gravity duality, the string in the bulk is dual to a flux tube between a quark-antiquark pair in the boundary field theory. We assume that the string is initially (quasi-)static. Perturbing one of the endpoints creates a large propagating wave on the string. The non-linear time-evolution produces a number of interesting phenomena: energy cascades, pair-creation of cusps, and evaporating regions on the string. If time permits, I will also talk about the string worldsheet as a simple model for gravity, chaos, out-of-time-order four-point functions, and segmented membranes.