Schedule and lectures

Lectures

• Andreas Blommaert - Introduction to double scaled SYK
  I will talk about the exact solution of the double scaled limit of the SYK model involving chord diagrams and an associated auxiliary quantum mechanics system. Furthermore I will discuss certain gravitational features of this model, and introduce a precise holographic dual.

• Marine De Clerck - Introduction to BKL theory
  This set of lectures will introduce the chaotic behaviour that arises in solutions of Einstein’s equation of General Relativity near a space-like singularity. Well-known near-singularity geometries, such as the interior of a Schwarzschild black hole, are quite fine-tuned in this regard. Seminal work by Belinski, Khalatnikov, Lifshitz (BKL) and others from the 60s and 70s, which we will review in detail, showed that the dynamics of generic solutions are in fact much more complex. These developments have lead to the fascinating realization that the chaos governing the near-singularity dynamics is of a quite special nature. After a brief overview of common characterizations of (quantum) chaos, we will delve into the peculiar symmetries appearing in this problem and find out about their effect on the chaotic aspects of the near-singularity evolution of the metric.

• Caroline Jonas - Quantum Cosmology: wavefunction of the universe, no-boundary proposal and gravitational path integral
  These lectures aim to provide a first introduction to quantum cosmology, the study of the very early universe including quantum effects. We will start by reviewing the early attempt to canonically quantize gravity. We will see how this led to the concept of a wavefunction of the universe together with the Wheeler-de Witt equation governing it. Then we will turn to the no-boundary and tunneling proposals and review the many successive endeavors to make these proposals concrete in simplified models. We will study in detail the Euclidean and Lorentzian gravitational path integrals, including some specific mathematical tools used in this context such as the Picard-Lefshetz theory of complex analysis. Finally and depending on time, we will  consider the approach of so called top-down quantum cosmology as well as the more recent developments related to the complex metrics criterion of Kontsevich and Segal.

• Chrysoula Markou - An introduction to string states and their interactions
  The spectrum of string theory comprises infinitely many physical states, which can collectively be visualized along Regge trajectories of increasing mass and spin. In these lectures, we will review traditional methodologies of constructing physical states in bosonic string theory and the rudiments of computing string scattering amplitudes. We will illustrate the framework with the example of a massless spin-2 state, which finds itself in closed-string spectra and whose low-energy self-interactions match those of the graviton of GR. Time permitting, we will discuss elements of a novel and efficient technology of excavating entire physical trajectories along with their interactions.

• Josh O'Connor and Ismael Ahlouche Lahlali - Coset symmetries and particle dynamics
  In these lectures we will encounter two different approaches to constructing particle Lagrangians from coset spaces of symmetry groups: (1) non-linear realisations, and (2) coadjoint orbits. The first method is more algebraic and has been used to understand theories of gravity in more detail, and the second involves more geometric definitions and has recently been used to shed light on BMS dynamics. At the level of particle Lagrangians these methods are equivalent, and we will demonstrate this by working out several examples. If time permits, we will discuss non-linear realisations leading to field theories, and a sketch of the Kirillov orbit method.

Schedule

TBA