Sommerfeld Theory Colloquium (ASC)

All the information we will ever obtain from the early universe is imprinted in the spatial correlations of primordial fluctuations at the hot Big Bang. I will explain how an influx of ideas from various areas of fundamental physics is providing us with new conceptual and practical tools to decode the physics of these primordial fluctuations. A thorough understanding of the fluctuations will give us insight into particle physics at high energies and may provide a window into the nature of spacetime itself.

One of the great insights of cryptography and computational complexity is the notion of computationally-bounded algorithms, which allow us to reason about properties that would otherwise be impossible to achieve. Could these ideas also be relevant to quantum information and quantum mechanics? In this talk, we discuss how computational thinking changes the landscape of quantum cryptography: What primitives can we construct, how definitions change, and what are the outstanding open problems. If time permits, we will also discuss new foundational questions on quantum information, motivated by cryptographic applications.

The gravitational two-body problem has been fundamental to physics since Newton's time. With the advent of gravitational wave astronomy and the anticipated third generation of gravitational wave detectors in the 2030s, there is an increasing need for high-precision predictions from Einstein's theory of gravity regarding the encounters of black holes and neutron stars in our universe. Fascinatingly, perturbative quantum field theory methods developed for high-precision predictions of elementary particle scattering at the LHC have proven remarkably efficient for this classical physics problem. This unexpected connection has led to inspiring synergies between collider and gravitational wave physics. In my talk, I will present our approach using a worldline quantum field theory inspired by string theory, which has emerged as the most efficient tool for quantifying the scattering of spinning black holes. We have achieved highest-precision perturbative results for the scattering angle, radiated energy, and recoil of such black hole encounters at the fifth order in Newton's gravitational coupling G. Our four-loop calculations have revealed a new class of mathematical functions related to Calabi-Yau manifolds, previously studied only in mathematics and string theory compactifications, appearing for the first time in a physical context: The radiated energy in gravitational waves at NNNNLO perturbation theory.

One of the great insights of cryptography and computational complexity is the notion of computationally-bounded algorithms, which allow us to reason about properties that would otherwise be impossible to achieve. Could these ideas also be relevant to quantum information and quantum mechanics? In this talk, we discuss how computational thinking changes the landscape of quantum cryptography: What primitives can we construct, how definitions change, and what are the outstanding open problems. If time permits, we will also discuss new foundational questions on quantum information, motivated by cryptographic applications.

All the information we will ever obtain from the early universe is imprinted in the spatial correlations of primordial fluctuations at the hot Big Bang. I will explain how an influx of ideas from various areas of fundamental physics is providing us with new conceptual and practical tools to decode the physics of these primordial fluctuations. A thorough understanding of the fluctuations will give us insight into particle physics at high energies and may provide a window into the nature of spacetime itself.

The gravitational two-body problem has been fundamental to physics since Newton's time. With the advent of gravitational wave astronomy and the anticipated third generation of gravitational wave detectors in the 2030s, there is an increasing need for high-precision predictions from Einstein's theory of gravity regarding the encounters of black holes and neutron stars in our universe. Fascinatingly, perturbative quantum field theory methods developed for high-precision predictions of elementary particle scattering at the LHC have proven remarkably efficient for this classical physics problem. This unexpected connection has led to inspiring synergies between collider and gravitational wave physics. In my talk, I will present our approach using a worldline quantum field theory inspired by string theory, which has emerged as the most efficient tool for quantifying the scattering of spinning black holes. We have achieved highest-precision perturbative results for the scattering angle, radiated energy, and recoil of such black hole encounters at the fifth order in Newton's gravitational coupling G. Our four-loop calculations have revealed a new class of mathematical functions related to Calabi-Yau manifolds, previously studied only in mathematics and string theory compactifications, appearing for the first time in a physical context: The radiated energy in gravitational waves at NNNNLO perturbation theory.

We present Denario, an AI multi-agent system designed to be a scientific research assistant. Denario can perform many different tasks, such as generating ideas, checking the literature, developing research plans, writing and executing code, making plots, and writing a scientific paper. Denario is built as a modular system, and therefore, can perform either very specific tasks, such as generating an idea, or carrying out end-to-end scientific analysis using cmbagent as a deep-research backend. In this talk, we describe Denario and its modules in detail and illustrate its capabilities by presenting multiple AI-generated papers generated by it. These papers cover many scientific disciplines, such as astrophysics, biology, biophysics, biomedical informatics, chemistry, material science, mathematical physics, medicine, and planetary science. Denario can also perform research combining ideas from different disciplines, and we illustrate it by showing a paper that applies methods from quantum physics and machine learning with astrophysical data. We publicly release the code at https://github.com/AstroPilot-AI/Denario. A Denario demo can also be run directly on the web at https://huggingface.co/spaces/astropilot-ai/Denario, and the full app is deployed on the cloud.

An appealing and challenging route towards engineering materials with specic properties is to find ways of designing or selectively manipulate materials, especially at the quantum level. We will provide an overview of how well-established concepts in the fields of quantum chemistry and materials have to be adapted when the quantum nature of light becomes important. We will pursue the question whether it is possible to create these new states of materials as groundstates of the system. To this end we will show how the emerging (vaccum) dressed states resembles Floquet states in driven systems. A particular appeal of light dressing is the possibility to engineer symmetry breaking which can lead to novel properties of materials, e.g coupling to circularly polarized photons leads to local breaking of time-reversal symmetry enabling the control over a large variety of materials properties (e.g.topology). We show that the new quantum electrodynamics density-functional formalism (QEDFT) can acocunt for those effects. We illustrate the realisation of those ideas in molecular complexes and 2D materials.

Tensor Network States, like matrix product or projected entangled pair states play an important role in both, quantum information theory and many-body physics. They offer a compact and efficient representation, enabling accelerated numerical computations and providing intuitive insights into many-body phenomena. In this talk, I will discuss how certain states can be efficiently prepared and manipulated using quantum devices, highlighting the use of local operations and classical communication. Tensor networks can also be used to efficiently describe quantum channels. I will also mention how those channels can be efficiently implemented as quantum circuits.

We present Denario, an AI multi-agent system designed to be a scientific research assistant. Denario can perform many different tasks, such as generating ideas, checking the literature, developing research plans, writing and executing code, making plots, and writing a scientific paper. Denario is built as a modular system, and therefore, can perform either very specific tasks, such as generating an idea, or carrying out end-to-end scientific analysis using cmbagent as a deep-research backend. In this talk, we describe Denario and its modules in detail and illustrate its capabilities by presenting multiple AI-generated papers generated by it. These papers cover many scientific disciplines, such as astrophysics, biology, biophysics, biomedical informatics, chemistry, material science, mathematical physics, medicine, and planetary science. Denario can also perform research combining ideas from different disciplines, and we illustrate it by showing a paper that applies methods from quantum physics and machine learning with astrophysical data. We publicly release the code at https://github.com/AstroPilot-AI/Denario. A Denario demo can also be run directly on the web at https://huggingface.co/spaces/astropilot-ai/Denario, and the full app is deployed on the cloud.

An appealing and challenging route towards engineering materials with specic properties is to find ways of designing or selectively manipulate materials, especially at the quantum level. We will provide an overview of how well-established concepts in the fields of quantum chemistry and materials have to be adapted when the quantum nature of light becomes important. We will pursue the question whether it is possible to create these new states of materials as groundstates of the system. To this end we will show how the emerging (vaccum) dressed states resembles Floquet states in driven systems. A particular appeal of light dressing is the possibility to engineer symmetry breaking which can lead to novel properties of materials, e.g coupling to circularly polarized photons leads to local breaking of time-reversal symmetry enabling the control over a large variety of materials properties (e.g.topology). We show that the new quantum electrodynamics density-functional formalism (QEDFT) can acocunt for those effects. We illustrate the realisation of those ideas in molecular complexes and 2D materials.

Tensor Network States, like matrix product or projected entangled pair states play an important role in both, quantum information theory and many-body physics. They offer a compact and efficient representation, enabling accelerated numerical computations and providing intuitive insights into many-body phenomena. In this talk, I will discuss how certain states can be efficiently prepared and manipulated using quantum devices, highlighting the use of local operations and classical communication. Tensor networks can also be used to efficiently describe quantum channels. I will also mention how those channels can be efficiently implemented as quantum circuits.

A hallmark of living systems is their ability to generate and maintain order under constant fluctuations. In cells, such order often emerges from chemomechanical pattern formation, where proteins both sense and remodel the geometry of the cell. Here, I will discuss how theoretical modeling and simulations can capture this feedback across different spatial scales, using three example systems: on the macroscopic scale of individual cells, we used optogenetic control over a chemomechanical protein system to control the shape of starfish oocytes and induce self-organized surface contractions in these cells. On the mesoscopic scale of synthetic vesicles, I will discuss how protein patterns can drive the motility of synthetic liposomes, providing a minimal mechanism to transform chemical energy into motion without molecular motors. Finally, on the intracellular nanometer scale, I will present a mechanism for pattern formation without active energy consumption that relies on curvature sensitivity of membrane-binding proteins. Looking forward, I will discuss data-driven avenues for systematically analyzing biological self-organization, with particular focus on bringing experiments and simulations closer together.

A hallmark of living systems is their ability to generate and maintain order under constant fluctuations. In cells, such order often emerges from chemomechanical pattern formation, where proteins both sense and remodel the geometry of the cell. Here, I will discuss how theoretical modeling and simulations can capture this feedback across different spatial scales, using three example systems: on the macroscopic scale of individual cells, we used optogenetic control over a chemomechanical protein system to control the shape of starfish oocytes and induce self-organized surface contractions in these cells. On the mesoscopic scale of synthetic vesicles, I will discuss how protein patterns can drive the motility of synthetic liposomes, providing a minimal mechanism to transform chemical energy into motion without molecular motors. Finally, on the intracellular nanometer scale, I will present a mechanism for pattern formation without active energy consumption that relies on curvature sensitivity of membrane-binding proteins. Looking forward, I will discuss data-driven avenues for systematically analyzing biological self-organization, with particular focus on bringing experiments and simulations closer together.

Already within the Standard Model, we expect that the fundamental scale of gravity, the scale where gravity becomes strong, is slightly lower than the Planck scale. Theories with extra dimensions or with many additional particle species enhance this effect and are motivated by giving a unified solution to the Hierarchy problem, Dark Matter, and neutrino masses. In this talk, we will discuss their phenomenology in low-energy experiments, their unique astrophysical signatures, and present recent experimental results.

Already within the Standard Model, we expect that the fundamental scale of gravity, the scale where gravity becomes strong, is slightly lower than the Planck scale. Theories with extra dimensions or with many additional particle species enhance this effect and are motivated by giving a unified solution to the Hierarchy problem, Dark Matter, and neutrino masses. In this talk, we will discuss their phenomenology in low-energy experiments, their unique astrophysical signatures, and present recent experimental results.

At a singularity the continuum description of spacetime breaks down and one can hope that the microscopic constituents will be revealed. Over 50 years ago, Belinski-Khalatnikov-Lifshitz (BKL) argued that the dynamics of spacetime close to the Big Bang singularity (or inside black holes) is chaotic and inhomogeneous. I will revisit the BKL scenario within a modern understanding of quantum chaos and holographic duality. I will argue that the remarkable modular symmetries that arise in the near-singularity dynamics suggests a dual description of the start of time as a so-called "primon gas", a description that is at once both simple and also connects with deep results from number theory.

In the development of animals, tissues self-organise starting from a single cell into lay- ers, shapes and patterns. This active mechanical process operates beyond the theoretical framework of reaction-diffusion equations such as Turing patterns. At the same time, combining active driving with careful mechanical design of a system is distinct route to pattern formation and artificial functionality. Here, I will begin by introducing vertex models, a tissue model where the two dimensional cell layer is approximated by a polygonal tilings. I will then how two types of active driving can generate function: First, for polar active materials, a coupling of activity to force, a.k.a. self-alignment, is generic. Governed by the activity-elasticity interactions, it generates either flocking or oscillatory dynamics depending on the boundary conditions of the tissue. Second, mechanochemical stress feedback in cell-cell junctions arises from the catch bond dynamics of the actomyosin cortex. It allows a junction to generate a contractile force that can overcome external pulling and thus allow for an active rear- rangement or T1. In vertex and continuum models, for strong enough feedback this gives rise to convergence-extension flows where the flow is opposite the direction of mechanical polarisation, effectively generating a negative viscosity state.

At a singularity the continuum description of spacetime breaks down and one can hope that the microscopic constituents will be revealed. Over 50 years ago, Belinski-Khalatnikov-Lifshitz (BKL) argued that the dynamics of spacetime close to the Big Bang singularity (or inside black holes) is chaotic and inhomogeneous. I will revisit the BKL scenario within a modern understanding of quantum chaos and holographic duality. I will argue that the remarkable modular symmetries that arise in the near-singularity dynamics suggests a dual description of the start of time as a so-called "primon gas", a description that is at once both simple and also connects with deep results from number theory.

In the development of animals, tissues self-organise starting from a single cell into lay- ers, shapes and patterns. This active mechanical process operates beyond the theoretical framework of reaction-diffusion equations such as Turing patterns. At the same time, combining active driving with careful mechanical design of a system is distinct route to pattern formation and artificial functionality. Here, I will begin by introducing vertex models, a tissue model where the two dimensional cell layer is approximated by a polygonal tilings. I will then how two types of active driving can generate function: First, for polar active materials, a coupling of activity to force, a.k.a. self-alignment, is generic. Governed by the activity-elasticity interactions, it generates either flocking or oscillatory dynamics depending on the boundary conditions of the tissue. Second, mechanochemical stress feedback in cell-cell junctions arises from the catch bond dynamics of the actomyosin cortex. It allows a junction to generate a contractile force that can overcome external pulling and thus allow for an active rear- rangement or T1. In vertex and continuum models, for strong enough feedback this gives rise to convergence-extension flows where the flow is opposite the direction of mechanical polarisation, effectively generating a negative viscosity state.

Ultra-High-Energy Cosmic Rays (UHECRs) are particles with energies up to $3times 10^20 eV$, originating from unknown sources and producing extensive air showers in Earth's atmosphere. In this talk, I will review the current status of UHECR observations, including the energy spectrum, mass composition, and anisotropy in their arrival directions. I will highlight how the knowledge of the Galactic Magnetic Field (GMF) of the Milky Way is crucial for identifying UHECR sources. Additionally, I will review recent models of the GMF. Finally, I will discuss the propagation of UHECRs from their sources through both intergalactic and galactic magnetic fields, and I will explore the prospects for future source identification.

Ultra-High-Energy Cosmic Rays (UHECRs) are particles with energies up to $3times 10^20 eV$, originating from unknown sources and producing extensive air showers in Earth's atmosphere. In this talk, I will review the current status of UHECR observations, including the energy spectrum, mass composition, and anisotropy in their arrival directions. I will highlight how the knowledge of the Galactic Magnetic Field (GMF) of the Milky Way is crucial for identifying UHECR sources. Additionally, I will review recent models of the GMF. Finally, I will discuss the propagation of UHECRs from their sources through both intergalactic and galactic magnetic fields, and I will explore the prospects for future source identification.

In a simple, constant environment does evolution continue forever? Does extensive diversification via small genetic and ecological differences? What are general evolutionary consequences of organismic complexity? Hints from long term laboratory evolution experiments and findings from genomic data of extensive within-species bacterial diversity motivate considering these questions. Several simple models of evolution with ecological feedback will be introduced, with the high dimensionality of phenotype space enabling analysis by statistical physics approaches.

In a simple, constant environment does evolution continue forever? Does extensive diversification via small genetic and ecological differences? What are general evolutionary consequences of organismic complexity? Hints from long term laboratory evolution experiments and findings from genomic data of extensive within-species bacterial diversity motivate considering these questions. Several simple models of evolution with ecological feedback will be introduced, with the high dimensionality of phenotype space enabling analysis by statistical physics approaches.

In driven open quantum matter, coherent many-body quantum dynamics, drive, and dissipation play equally significant roles. These systems span a wide range of examples, including cold atomic gases, exciton-polaritons in solid state, and quantum devices designed for quantum information applications. These setups break the conditions of thermodynamic equilibrium on the microscopic scale, prompting questions about how this impacts macroscopic behavior, such as phases and phase transitions. We examine two key points: First, we showcase that a minor out-of-equilibrium perturbation on the microscopic level can lead to substantial macroscopic effects, including the emergence of novel non-equilibrium universality classes. This paves the way to active quantum matter scenarios in solid state physics. Second, we argue that drive and dissipation can be used constructively to maintain or even create fragile quantum mechanical correlations such as phase coherence, entanglement or topological order by carefully engineering the system. A topological quantum phase transition far from equilibrium can be induced in this way, exhibiting intriguing analogies to the problem of directed percolation.

In driven open quantum matter, coherent many-body quantum dynamics, drive, and dissipation play equally significant roles. These systems span a wide range of examples, including cold atomic gases, exciton-polaritons in solid state, and quantum devices designed for quantum information applications. These setups break the conditions of thermodynamic equilibrium on the microscopic scale, prompting questions about how this impacts macroscopic behavior, such as phases and phase transitions. We examine two key points: First, we showcase that a minor out-of-equilibrium perturbation on the microscopic level can lead to substantial macroscopic effects, including the emergence of novel non-equilibrium universality classes. This paves the way to active quantum matter scenarios in solid state physics. Second, we argue that drive and dissipation can be used constructively to maintain or even create fragile quantum mechanical correlations such as phase coherence, entanglement or topological order by carefully engineering the system. A topological quantum phase transition far from equilibrium can be induced in this way, exhibiting intriguing analogies to the problem of directed percolation.

This talk will overview the history of primordial black hole (PBH) research from the first papers around 50 years ago to the present time. I will first discuss their possible formation mechanisms, including critical collapse from inflationary fluctuations and various types of phase transition. I will then describe the numerous constraints on the number of PBHs from various quantum and astrophysical processes, this being the main focus of PBH research until recently. In the last decade there has been a shift of emphasis to the search for evidence for PBHs 13 what I term the bright side. So the final part of my talk will present this evidence, with particular emphasis on their possible role as dark matter candidates, sources of gravitational waves and seeds for supermassive black holes and early cosmic structures.

We will review the beginning of experimental and theoretical studies of moire systems and their evolution up to present. We will show how thousands of p orbitals in a moire unit cell of graphene can create single Heavy fermion at moire scale, and how the interaction between such fermions can lead to a perfect quantum simulator of an Anderson model. We will then present a catalogue of possible twistable materials and show how a huge variety of strongly interacting models can be realized in twisted homo and hetero twiste bilayers and multilayers of these materials.

This talk will overview the history of primordial black hole (PBH) research from the first papers around 50 years ago to the present time. I will first discuss their possible formation mechanisms, including critical collapse from inflationary fluctuations and various types of phase transition. I will then describe the numerous constraints on the number of PBHs from various quantum and astrophysical processes, this being the main focus of PBH research until recently. In the last decade there has been a shift of emphasis to the search for evidence for PBHs 13 what I term the bright side. So the final part of my talk will present this evidence, with particular emphasis on their possible role as dark matter candidates, sources of gravitational waves and seeds for supermassive black holes and early cosmic structures.

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.

We will review the beginning of experimental and theoretical studies of moire systems and their evolution up to present. We will show how thousands of p orbitals in a moire unit cell of graphene can create single Heavy fermion at moire scale, and how the interaction between such fermions can lead to a perfect quantum simulator of an Anderson model. We will then present a catalogue of possible twistable materials and show how a huge variety of strongly interacting models can be realized in twisted homo and hetero twiste bilayers and multilayers of these materials.

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.

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.

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.

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.

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.

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.

I will discuss recent progress in the study of cosmological applications of string compactifications with stabilised moduli, focusing in particular on inflation, reheating and dark energy.