Week 21.10.2024 – 27.10.2024

These lectures will review recent developments surrounding the infrared sector of gravity in (3+1)-dimensional asymptotically flat spacetimes (AFS). In the first part of the course we will introduce soft theorems which govern the low-energy scattering of massless particles such as photons and gravitons. We will explain how these are related to classical observables known as memory effects and discuss their application to computing infrared-finite collider observables and gravitational waveforms. In the second part, we will introduce the notion of asymptotic or large-gauge symmetries and use it to derive the infinite-dimensional asymptotic symmetry algebra of (3+1)-dimensional AFS, also known as the BMS algebra. We will show that the conservation laws associated with these symmetries are equivalent to the Weinberg soft graviton theorem. Time-permitting, we will discuss some implications of these ideas for non-AdS holography.

Machine learning and related computational methods have become substantially more powerful and are already applied in many areas of science. In the future, they are likely to change scientific research profoundly. In this talk I will be discussing two ways in which machine learning can be helpful in physics: solving differential equations and model building. I will attempt to explain the basic ideas behind these applications and present some recent examples, including inflationary model building, finding string models with certain prescribed properties and computing the masses of fermions from string theory.

The original singularity theorems of Penrose and Hawking have, in their hypotheses, pointwise energy conditions violated by some classical and all quantum fields. If we want to extend their validity to semiclassical gravity, these conditions have to be replaced by weaker ones. In this talk I will first discuss recent results for singularity theorems with weakened energy conditions, some of which are obeyed by quantum fields. Then I will argue for the need of singularity theorems with worldvolume averaged energy conditions both in the timelike and the null case. For each case I will present progress and open questions.

The numerical S-matrix Bootstrap aims at establishing non-perturbative universal bounds on physical observables that can be extracted from scattering amplitudes in any dimension. In the first part of the talk, I will review our past explorations of the space of supergravity amplitudes and their connection to String/M theory. I will discuss the universal bounds on the first non-universal correction to sugra amplitudes, and how the extremal solution is compatible with clustering in the Born regime, and with the Quantum Regge growth hypothesis. In the second part of the talk I will report on a first Bootstrap exploration of multi-particle scattering. I will focus on the simplest non-integrable S-matrix describing the scattering of branons on the world-sheet of confining strings in three dimensions.

In this talk, I will discuss a novel strategy to fit experimental data using an amplitude ansatz satisfying the constraints of Analyticity, Crossing, Unitarity, and UV completeness. The fit strategy requires both the use of S-matrix Bootstrap methods and non-convex Particle Swarm Optimization (PSO) techniques. As a proof of principle, I will focus on $\pi\pi$ scattering. Using this procedure, I will show how to construct numerically a full-fledged scattering amplitude that fits the available experimental and lattice data, and that features all the known QCD spectrum with quantum numbers $I^G=0^+,1^+$ below 1.4 GeV, plus an additional surprise.