In heavy-ion collisions at ultra-relativistic energies, nuclear matter is subject to extreme conditions of temperature and density. A crossover happens, and nuclear matter transits into an almost perfect liquid that exhibits properties similar to those of a quantum fluid, the Quark Gluon Plasma (QGP). In a manner similar to the Rutherford experiment, where alpha particles were short-range probes of the atom, revealing the existence of the nucleus, we use energetic quarks and gluons as high-resolution probes of the QGP to study its microscopic structure. I will discuss the status and main open questions of the field.

In the setting of the wave equation on asymptotically anti-de Sitter spacetimes, it is possible to define an operator which maps Dirichlet data of solutions to corresponding Neumann data at the conformal boundary. The Dirichlet-to-Neumann map (or the boundary-to-boundary propagator) is conjectured to determine the bulk metric up to trivial transformations. In this talk I will report on recent progress on this question, based on the proof that the Dirichlet-to-Neumann map is a fractional power for the boundary metric in a suitable sense. In particular I will discuss the case of Einstein AdS spaces in which case we can prove stronger statements (joint work with Alberto Enciso and Gunther Uhlmann).

Tailored light excitation and nonlinear control of lattice vibrations have emerged as powerful strategies to manipulate the properties of quantum materials out of equilibrium. Generalizing the use of coherent phonon-phonon interactions to nonlinear couplings among other types of collective modes would open unprecedented opportunities in the design of novel dynamic functionalities in solids. For example, the collective excitations of magnetic order –magnons– can carry quantum information with little energy dissipation, and their coherent and nonlinear control would provide an attractive route to achieve collective-mode-based information processing and storage in forthcoming spintronics and quantum information science.

In this talk, I will show that intense terahertz (THz) fields can initiate processes of magnon up-conversion and magnon mixing mediated by an intermediate magnetic resonance. By using a suite of advanced spectroscopic tools, including a newly demonstrated two-dimensional THz polarimetry technique, we unveil these anharmonic magnon coupling phenomena in a canted antiferromagnet. These results demonstrate a route to inducing desirable energy transfer pathways between coherent magnons in solids and pave the way for a new era in the development of ultrafast control of magnetism.