This course taught by Adrián Pérez-Salinas (Leiden University The Netherlands).

By this point it is fairly well known that symmetries can be generalised in many ways including the case where the topological operator that generates the symmetry does not have an inverse.

Contents: Gravitational wave memory is a non-linear prediction of general relativity that informs us about the energy fluxes emitted by gravitati.

Results from LHAASO and HAWC have revealed a new picture about the gamma-ray sky reaching energies above hundreds of TeV.

In this talk we discuss the construction of a broad class of asymptotic conditions for the gravitational field in three dimensions that reproduce the properties of the Ablowitz-Kaup-Newell-Segur (AKNS) integrable system.

Chiral symmetry is hard to engineer on the lattice. The origin of this problem can be traced to the Nielsen Ninomiya theorem which in its most naive form forbids the existence of unpaired Weyl fermions on the lattice.

Detecting Gravitational Waves (GWs) across a wide range of frequencies will certainly allow us to uncover new phenomena.

The unprecedented energy of the Large Hadron Collider (LHC) offers us a once-in-a-generation opportunity to explore the nature of the electroweak phase transition (EWPT) in the early universe.

Ultralight dark matter can induce oscillations in fundamental constants of nature such as the fine-structure constant the strength of the strong interaction and particle masses.

Axion-like particles (ALPs) appear in several well-motivated extensions of the Standard Model. In this talk we will discuss collider constraints on axion-like particles.