In this talk, I will explore the fascinating connections between string theory and quantum field theory, focusing on what we have learned from studying string scattering amplitudes. These insights have not only deepened our understanding of particle interactions but have also led to significant advancements in quantum field theory itself. To set the stage, I will introduce string theory, highlighting its foundational principles and its relationship to low-energy quantum field theories that describe the fundamental forces of nature. Building on this, I will delve into three key concepts 14massive gravity, the double copy framework, and twisted cohomology 14all of which have roots in string theory or have been profoundly influenced by it. I will explain how massive gravity emerges as a natural extension in the context of string theory and how the double copy framework elegantly connects gauge theories with gravity, offering a unifying perspective. Twisted cohomology, a sophisticated mathematical tool, will be discussed in relation to the structure of scattering amplitudes and its role in uncovering deeper symmetries. Finally, I will illustrate how these ideas impact our understanding of scattering amplitudes in quantum field theories and how they are applied to describe physics across a wide range of energy scales 14from the low-energy behavior of known particles to the high-energy frontier. Through these examples, I aim to show how string theory serves as a powerful lens for reimagining and advancing our understanding of particle physics.

I will discuss Effective Field Theories that can originate from microscopic unitary theories, and their relation to moment theory. I will show that massive gravity, theories with isolated massive higher-spin particles, and theories with very irrelevant interactions, don't posses healthy UV completions, and I will show how Vector Meson Dominance follows from such first principles.

Our search for a quantum theory of gravity is aided by a unique and perplexing feature of the classical theory: General Relativity already knows" about its own quantum states (the entropy of a black hole), and about those of all matter (via the covariant entropy bound). The results we are able to extract from classical gravity are inherently nonperturbative and increasingly sophisticated. Recent breakthroughs include a derivation of the entropy of Hawking radiation, a computation of the exact integer number of states of some black holes, and the construction of gravitational holograms in our universe using techniques from single-shot quantum communication protocols.

Gravitational waves open a new window into our universe. In this colloquium we discuss particle theorists' perspective on calculations directly relevant for gravitational-wave emission from compact objects, which is rooted in quantum field theory and builds on the idea that gravitational interactions are mediated by spin-2 particles. After reviewing some of the remarkable advances in our understanding of scattering amplitudes and in our ability to evaluate them, we show how these ideas produce state of the art results in weak-field fully-relativistic calculations for gravitational wave observables, including for the astrophysical binary black hole inspiral problem.

Understanding dark energy and black holes remain a great challenge to fundamental physics. In this talk I will review the difficulties and explore some new and speculative approaches.

I will describe recent developments on the (numerical) computation of energy levels of various systems by the quantum mechanical bootstrap. The main way the bootstrap works is by using constraints that arise from positive matrices. Part of the goal is to turn the bootstrap problem into a problem that can be solved by semi-definite programming methods. I will describe how this method leads to solutions of the spectrum of various systems and will describe some additional applications of this way of solving problems to the study of quantum spin chains.

Interesting erasure phenomena arise from interactions between lower-dimensional and higher-dimensional objects and impact cosmology and fundamental physics. In the first part of the colloquium, I will examine the case for topological defects, revealing insights into the interactions of magnetic monopoles, cosmic strings, and domain walls.

For objects like cosmic or QCD flux strings, encounters with domain walls or D-branes result in erasure through coherence loss during collisions, introducing a new string break-up mechanism. The collisions between magnetic monopoles and domain walls in an SU(2) gauge theory lead to monopole erasure, which is pivotal in post-inflationary phase transitions and potentially solves the cosmological monopole problem. Simulations show that strings or monopoles cannot penetrate domain walls. Entropy-based arguments highlight the significance of the erasure phenomena that can produce correlated gravitational waves and electromagnetic radiation, impacting cosmology and astrophysics.

The second part of the colloquium focuses on the saturation of unitarity and the emergence of Saturons. These self-sustained objects, which reach the maximal entropy allowed by unitarity, resemble black holes.

I discuss a "black hole-saturon" correspondence in a renormalizable SU(N) invariant theory. Despite lacking gravity, saturons show features like an information horizon, Bekenstein-Hawking entropy, thermal evaporation, and a characteristic information retrieval time. This correspondence has significant implications for black hole physics and saturated systems. We will examine recent results on saturon mergers, vortices in black holes, and primordial black holes, offering new perspectives on fundamental theory and observations.

One of the major problems of computational chemistry is the ab initio prediction of energies and properties of molecules. The electronic Schrödinger equations provides the in-principle solution, but because of intrinsic difficulties associated with the singular and long-ranged Coulomb interaction, this remains an extremely challenging task numerically. Here we outline a formalism called transcorrelation which provides a route out of the difficulties, whilst itself creating new problems (which have stumped the community for decades). We outline our work of the past few years in tackling these new problems, and show that the formalism has the potential to transform our ability to solve the Schrödinger problem in a general manner. In particular, by eliminating the Coulomb singularities, we show we can achieve both basis-set converged results, as well as thermodynamic limit results, with far fewer resources and less sophisticated many-body theories. Prospects to extend this methodology in the context of quantum computing will also be mentioned.

One of the simplest ways to make gauge fields massive is to add them a mass "by hand". Intuitively, one could expect that the corresponding massless theory would then be easy to recover. Yet, conventional methods indicate that such a limit is singular. In this talk, we will explore the massless limits of several massive gauge theories. We will identify the source of the apparent discontinuities and show that they are, in fact, simply an artifact of the perturbative approach. Then, we will discuss the consequences of this study on the relations between different gauge fields. Finally, we will conclude with a comment on the latest insights about these theories and their prospects.

Learning algorithms using deep neural networks are currently having a major impact on basic sciences. The physics of complex quantum systems is no exception, with multiple applications that constitute a new field of research. Examples include the representation and optimization of wave functions of quantum systems with large numbers of degrees of freedom (neural quantum states), the determination of wave functions from measurements (quantum tomography), and applications to the electronic structure of materials, such as the determination of more precise density functionals or the learning of force fields to accelerate molecular dynamics simulations. I will survey some of these applications, with an emphasis on neural quantum states.