Random matrices are ubiquitous in modern theoretical physics and provide insights on a wealth of phenomena, from the spectra of heavy nuclei to the theory of strong interactions or random two dimensional surfaces. The backbone of all the analytical results in matrix models is their 1/N expansion (where N is the size of the matrix). Despite early attempts in the '90, the generalization of this 1/N expansion to higher dimensional random tensor models has proven very challenging.

I will review the status of observations  and modelling of intergalactic magnetic fields (IGMF), with an update on recent results from gamma-ray searches. These fields, present in the voids of the Large Scale Structure (LSS) are either relics from the Early Universe or are produced in result of the star formation feedback on the LSS. I will put the observational results in the context of to possible mechanisms of generation and evolution of the IGMF.

A model suited for calculating correlation functions in QCD from the ultraviolet to the infrared is reviewed. The model consist in standard Faddeev-Popov Lagrangian for Landau gauge with an extra mass term for gluons. It is shown that once this mass term is included, two and three point correlation functions can be calculated with good precision at one-loop order even at very low momenta in the quenched approximation. After that, the inclusion of quarks is analyzed.

We study a very light dilaton, arising from a scale-invariant ultraviolet theory of the Higgs sector in the standard model  of particle physics. Imposing the scale symmetry below the ultraviolet scale of the Higgs sector, we alleviate the fine-tuning problem associated with the Higgs mass. When the electroweak symmetry is spontaneously broken radiatively  a la Coleman-Weinberg, the dilaton develops a vacuum expectation value away from the origin to give an extra contribution  to the Higgs potential so that the Higgs mass is around the electroweak scale.

LISA may be able to detect the gravitational waves from a first order phase transition at the electroweak scale. We present results from a large campaign of simulations studying a model of such phase transitions, and determine the shape of the power spectrum with unparalleled accuracy. We make concrete predictions of the detectability of sound waves from such a scenario, and note that an accurate measurement could place constraints on the underlying phase transition parameters.