Schedule and lectures

Schedule (preliminary)

Lectures

• Jackson Fliss - Energy conditions in classical and quantum field theory, and semi-classical gravity
  Energy conditions play an important role in gravitational physics: through the Einstein equation, constraints on the local distribution of energy translate to constraints on physically realizable spacetimes. I will review well known classical energy conditions and their implications for gravitational solutions, such as the celebrated Hawking and Penrose singularity theorems. This topic becomes both richer and more subtle when considering quantum fields coupled to gravity as even the simplest quantum theories violate local energy conditions. I will discuss directions for suitably constraining energy densities in quantum field theories, including averaging over regions of spacetime and bounds relating energy and quantum information. I will explore implications of these bounds for quantum field theory coupled to gravity as an effective theory.

• Javier Subils - Holographic confinement and its probes
  Confinement and the existence of a mass gap are among the most challenging phenomena to understand in quantum field theory. One of the strengths of holography is its ability to offer an intuitive (geometric) realization of confinement. In these lectures, after introducing the AdS/CFT correspondence, I will explain how confinement can be "understood" via the gravitational dual of a gauge theory. In particular, I will review the physics of some of the most iconic confining holographic setups, such as the Witten soliton or the Klebanov–Strassler solution. 

• Matilda Delgado - From Symmetries to Branes: Dynamical Implications of the Cobordism Conjecture
  This lecture series will review a core principle of the Swampland program: that consistent theories of quantum gravity forbid exact global symmetries. We begin with a pedagogical overview of this conjecture, its motivation from black hole physics, and its modern generalizations to higher-form and other generalized global symmetries. The second half of the course will focus on the Cobordism Conjecture, which provides a sharp topological perspective on this principle. We will explain how cobordism classes can be associated with generalized symmetries in the low-energy theory, and how quantum gravity is expected to eliminate these symmetries. This leads to the prediction of new extended objects, whose properties and dynamics we will examine in detail.

• Simon Ekhammar - Introduction to Quantum Spectral Curve and the Spectrum of N=4 Super Yang-Mills
  Finding the full spectrum of a four-dimensional conformal field theory is a highly challenging problem. Excitingly, there has been tremendous progress in achieving this goal in planar four-dimensional maximally supersymmetric Yang-Mills theory (N=4 SYM), a theory which, through the AdS/CFT correspondence, is also dual to strings propagating on AdS₅ × S⁵. The key to this progress lies in the surprising fact that planar N=4 SYM appears to be integrable, allowing the use of powerful tools not typically at our disposal. In these lectures, I will first describe how to use integrability to find the spectrum of rational spin chains, one of the simplest integrable models. Thereafter, building on this foundation, we will attack N=4 SYM, exploring the most modern formulation of integrability in N=4 SYM: the Quantum Spectral Curve.