In this talk, I will discuss the applications of cavity electrodynamics for controlling many-body electron systems. The focus will be on achieving strong coupling between cavities and collective excitations of interacting electrons at Terahertz and IR frequencies. As a specific example I will consider a cavity platform based on a two dimensional electronic material encapsulated by a planar cavity consisting of ultrathin polar van der Waals crystals. I will also discuss how metallic mirrors sandwiching a paraelectric material can modify the transition into the ferroelectric state. Finally, I will review a general question of theoretically describing ultrastrong coupling waveguide QED. I will present a novel approach to this problem based on a non-perturbative unitary transformation that entangles photons and matter excitations. In this new frame of reference, the factorization between light and matter becomes exact for infinite interaction strength and an accurate effective model can be derived for all interaction strengths.

It is commonly recognized that scientific discoveries result in new technologies. In this talk we will discuss the reverse: behind every conceptual breakthrough lies some technological advance. To illustrate this point, we will review how modern progress in optical technologies is revolutionizing our understanding of quantum matter. We will discuss experiments that showed that we can optically control materials, and even suggest light-induced superconductivity. We’ll delve into a new type of magnetism, discovered in layered materials using sensitive light reflection experiments rather than measurements of magnetization. We’ll cover how we can use optical lattices with tunable geometries to create several paradigmatic models of electron systems and shed light onto their puzzling properties. We will finally discuss why understanding technology is important for theoretical physicists.

Recent experiments suggest the phenomenon of light induced superconductivity above Tc in two different materials: fullerene superconductor K3C60 and high Tc cuprate YBCO. I will discuss the distinct phenomena taking place in these systems. In K3C60, the unusual character of electron-phonon interactions results in enhanced BCS pairing through optical driving and the slow relaxation of superconducting correlations after they have been created. In YBCO the light induced state is short lived and its properties can be explained from the perspective of a Floquet material. I will present a general theoretical framework for understanding Floquet materials, in which the pump-induced oscillations of a collective mode lead to the parametric generation of excitation pairs. This can result in features such as photo- induced edges in reflectivity, enhancement of reflectivity, and even light amplification.

The density of states of a unitary quantum field theory is known to have a universal behavior at high energy. In two dimensions, this behavior is described by the Cardy formula. When the theory has symmetry, it is interesting to find out how the Hilbert space is decomposed into irreducible representation of the symmetry. In this talk, I will derive universal formulas for the decomposition of states at high energy with respect to both internal global symmetry and spacetime symmetry. The formulae are applicable to any unitary quantum field theory in any spacetime dimensions. As a byproduct, we resolve one of the outstanding questions on the stability of non-abelian black holes. We will also derive the high energy asymptotic behavior of correlation functions. (Based on work with Nathan Benjamin, Daniel Harlow, Monica Kang, Jaeha Lee, Sridip Pal, David Simmons-Duffin, Zhengdi Sun, and Zipei Zhang.)

Although predictions of quantum gravity are typically at extremely high energy, several non-trivial constraints on its low energy effective theory have been found over the last decade or so. I will start by explaining why the unification of general relativity and quantum mechanics has been difficult. After introducing the holographic principle as our guide to the unification, I will discuss its use in finding constraints on symmetry in quantum gravity. I will also discuss other conjectural constraints on low energy effective theories, collectively called swampland conditions, and their consequences.

We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient computation. We study the correlation between quantum chaos diagnostics, the circuit expressibility and the optimization of the control parameters.

Fluid turbulence is a major unsolved problem of physics exhibiting an emergent complex structure from simple rules. We will briefly review the problem and discuss three avenues towards its solution: field theory, holography and machine learning.

The amazing and mysterious laws of the quantum world will be outlined: superposition, entanglement and no cloning. Their impact on science and technology will be discussed, including quantum teleportation, secure quantum communication, quantum money, powerful quantum algorithms and quantum machine learning.

Gravitational wave signals from coalescing binary black holes are detected, and analyzed, by using large banks of template waveforms. The construction of these templates makes an essential use of the analytical knowledge of the motion and radiation of gravitationally interacting binary systems. A new angle of attack on gravitational dynamics consists of considering (classical or quantum) scattering states. Modern amplitude techniques have recently given interesting novel results. These results are reaching a level where subtle conceptual issues arise (quantum-classical transition, radiative effects versus conservative dynamics, massless limit,...).

The observation of gravitational wave signals by the two interferometers of the Laser Interferometer Gravitational-Wave Observatory (LIGO), and by the Virgo interferometer, has brought the first direct evidence for the existence of black holes, and has also been the first observation of gravitational waves in the wave-zone. After reviewing the historical path that led to our understanding of gravitational waves and black holes, the colloquium will present the theoretical developments on the motion and gravitational radiation of binary black holes that have been crucial in interpreting the LIGO-Virgo

events as being emitted by the coalescence of two black holes.