These lecture notes, based on the course given at IPhT in November/December 2023, provide a pedagogical introduction to the study of strings in AdS$_3$ backgrounds supported by NSNS flux from the worldsheet perspective, including a number of updates incorporating recent results. We attempt to give a self-contained overview of the state-of-the-art understanding of this topic, describing key aspects of its 25-year-long rich history alongside some important recent developments, with an emphasis on the computation of worldsheet correlation functions involving spectrally flowed insertions.
These lecture notes provide an introduction to the generation of initial conditions for cosmological N-body simulations. Starting from the definition and properties of Gaussian random fields, we discuss their role in cosmology and the efficient generation of such fields using Fourier methods. The Vlasov-Poisson system is introduced as the governing framework for cold collisionless matter, and its solution via characteristics and Lagrangian perturbation theory (LPT) is detailed. We discuss the use of LPT for initializing N-body simulations, emphasizing the importance of high-order LPT and late-time starts to minimize truncation and discreteness errors. Finally, we discuss time integration schemes, including PT-informed integrators, and their role in accurately evolving the system. These notes aim to bridge the gap between theoretical perturbation methods and practical simulation techniques.
We guide a competent programmer through the programming of a quantum circuit simulator, supporting quantum logic gates with arbitrary control qubits on 20+ qubits, assuming no previous knowledge of quantum computing. We explain qubit-wise multiplication for updating the state vector; how to compute partial traces on arbitrary subsets of qubits to find reduced density matrices; and computing qubit phase and purity. A sample implementation in JavaScript is provided, which also demonstrates how to compute von Neumann entropy, concurrence (to quantify entanglement), and magic, with source code much smaller and easier to study than other popular software packages.
Modern cosmology is based on the cosmological principle, which states that the Universe is statistically homogeneous and isotropic. When applied in its strict – rather than statistical – sense, the cosmological principle leads to the Friedmann–Lemaître–Robertson–Walker (FLRW) model, which serves as background spacetime. This background is used to predict: (1) the dynamics of cosmic expansion; and (2) the kinematics of light propagation through the Universe, which dictates the interpretation of cosmological observations. In this lecture, we shall discuss the performance of the FLRW model for those purposes, and present some results on the so-called backreaction and fitting problems.
