The (3+1)D dilute Glasma is a novel framework for the computation of rapidity-dependent early-time observables in relativistic heavy-ion collisions. First, I discuss the QCD phase diagram and the extremely successful class of experiments called heavy-ion collisions performed at RHIC and LHC. I then show how the Glasma, the first stage after a collision of relativistic nuclei, emerges in the Color Glass Condensate effective theory for high energy QCD. The dynamics of the Glasma are governed by the classical Yang-Mills equations, which I will solve for longitudinally extended sources, employing the dilute approximation. I obtain an analytic expression for the energy-momentum tensor of the Glasma as a function of rapidity. This opens up new insights into the longitudinal dynamics of the Glasma, which have previously been notoriously hard to simulate. Finally, I will show some numerical results for early-time observables in relativistic heavy-ion collisions obtained in the dilute Glasma framework.

We study asymptotic symmetries for 3d Chern-Simons theory as a gauge theory of so(3,2), sl_4 and sl_5 algebras. For the near horizon boundary conditions we present solutions from several projectors from Chern-Simons to the metric formulation. We also study the classification according to so(3,2) one parameter subgroups and classify obtained solutions.

Phase separation plays a crucial role in determining the self-assembly of biological and soft matter systems. In the former case, liquid-liquid phase separation inside a cell leads to the formation of various macromolecular aggregates. The interaction among these aggregates is soft and the particles are generally modelled by ultrasoft particles. We have studied the phase separation dynamics of binary mixture of ultrasoft particles (with species A and B). When quenched to a lower temperature below critical temperature, the system undergoes a phase separation into an A-and a B-rich phase. In detailed and extensive molecular dynamics simulations we have identified the critical point. When cooling the system the domains of the two components grow in a power-law manner with an exponent α = 1/3) which is consistent with the Lifshitz-Slyozov law. In a subsequent step we have exposed the system – as it is cooled down to low temperatures - to shear and have studied the stress response of the system to the these external forces; in their presence the domains grow with exponents α = 4/3 and α = 1/3 in the shear and the gradient direction, respectively. In particular we have analysed how spatial inhomogeneities (which are characteristic for the phase separation scenario) evolve under the shear forces.

The wave maps equation first appeared in particle physics as a nonlinear sigma model and the Yang-Mills equations originated from gauge theory for the strong interaction. They constitute prototypes of nonlinear geometric wave equations which, remarkably, have an explicit solution that forms a singularity in finite time. To determine the significance of these blowup solutions for the underlying dynamics, one studies their stability. In this talk, we give an elementary introduction to the mathematical analysis of blowup in both model equations and present some new stability results.

Sub-wavelength arrays of quantum emitters offer an interesting approach to coherent light-matter interfacing, using ultracold atoms or two-dimensional solid-state quantum materials. The combination of collectively suppressed photon-losses and emerging optical nonlinearities due to strong photon-coupling to mesoscopic numbers of emitters holds promise for generating nonclassical light and engineering effective interactions between freely propagating photons. In my talk I will describe the interaction between photons and a specific configuration of two-level atoms, namely two parallel 2D arrays individually acting like mirrors and together forming a cavity-like system. The long confinement of photons in this system results in an accumulation of correlation between the photons, revealing their strong effective interaction mediated by the atoms. While most studies have thus far relied on numerical simulations, I will furthermore describe a Green's function approach that permits analytical investigations of the nonlinear processes of the system. The approach yields intuitive insights into the nonlinear response of the system and offers a promising framework for a systematic development of a many-body theory for interacting photons and many-body effects on collective radiance in two-dimensional arrays of quantum emitters.

We apply machine learning to understand fundamental aspects of holo- graphic duality, specifically the entropies obtained from the apparent and event horizon areas. We show that simple features of only the time series of the pressure anisotropy can predict the areas of the apparent and event horizons in the dual bulk geometry at all times. Given that simple Vaidya-type metrics constructed just from the apparent and event horizon areas can be used to approximately obtain unequal time correlation functions, we argue that the corresponding entropy functions are the measures of information that need to be extracted from simple one-point functions to reconstruct specific aspects of correlation functions of the dual state with the best possible approximations.