Prof. Frank Verstraete and Celine Broeckaert invite you to a talk celebrating 100 years of quantum and the launch of their book: Why Nobody Understands Quantum Physics. The talk is at the Royal Institution (21 Albemarle St, London W1S 4BS). Please RSVP at RSVPEVENTS_at_MACMILLAN.COM.

informal seminar and dialogues with Mike in our historical rooms.

The period between inflation and nucleosynthesis can last for thirty orders of magnitude of time and represent half the lifetime of the universe on a logarithmic scale. But yet, there are minimal observational constraints on this epoch. String cosmologies motivate a rich set of modifications from the standard radiation-dominated post-inflationary assumption of Lambda CDM. In particular, string cosmology suggests the likelihood of moduli-dominated cosmologies through kination, tracker and matter epochs. I review the possible scenarios and observational possibilities, including a novel percolation scenario for formation of cosmic string networks.

I will describe work on a universal relevant deformation that takes local unitary 3d N=4 superconformal field theories to topological quantum field theories. For example, I will describe how Abelian mirror symmetry is related to generalizations of level rank duality, and I will also discuss some more general statements and constraints that arise via t Hooft anomaly matching.

Symmetry plays an important role in quantum systems: it can constrain the dynamics, give rise to selection rules, and provide computation methods in quantum computers. In recent years there are also new types of symmetries called generalized symmetries discovered in many quantum systems, including non-invertible symmetry and higher group symmetry. These lectures will be about symmetries in various quantum systems and their applications such as constraints on the low energy dynamics. Examples will be discussed in the lectures include quantum mechanics systems, gauge theories, lattice models, and the symmetry includes ordinary and higher form symmetry as well non-invertible symmetry.

Rare macroscopic fluctuations leading to large deviations in many-body systems have attracted significant attention in recent years. In this talk we present an exact solution to such a problem - the emptiness formation in one-dimensional quantum polytropic gases characterized by an arbitrary polytropic index \gamma, which defines the equation of state P ~ \rho^\gamma, where P is the pressure and \rho is the density. The problem consists of determining the probability of spontaneous formation of an empty interval in the ground state of the gas. In the limit of a macroscopically large interval, this probability is dominated by an instanton configuration. By solving the hydrodynamic equations in imaginary time, we derive the analytic form of the emptiness instanton. This solution is expressed as an integral representation analogous to those used for correlation functions in Conformal Field Theory. Prominent features of the spatiotemporal profile of the instanton are obtained directly from this representation and will be discussed in the context of limit shape phenomena. [1] A.G. Abanov and D.M. Gangardt, arXiv:2412.1168

Symmetry plays an important role in quantum systems: it can constrain the dynamics, give rise to selection rules, and provide computation methods in quantum computers. In recent years there are also new types of symmetries called generalized symmetries discovered in many quantum systems, including non-invertible symmetry and higher group symmetry. These lectures will be about symmetries in various quantum systems and their applications such as constraints on the low energy dynamics. Examples will be discussed in the lectures include quantum mechanics systems, gauge theories, lattice models, and the symmetry includes ordinary and higher form symmetry as well non-invertible symmetry.

Symmetry plays an important role in quantum systems: it can constrain the dynamics, give rise to selection rules, and provide computation methods in quantum computers. In recent years there are also new types of symmetries called generalized symmetries discovered in many quantum systems, including non-invertible symmetry and higher group symmetry. These lectures will be about symmetries in various quantum systems and their applications such as constraints on the low energy dynamics. Examples will be discussed in the lectures include quantum mechanics systems, gauge theories, lattice models, and the symmetry includes ordinary and higher form symmetry as well non-invertible symmetry.

Orbifolding the N=4 SYM theory naively breaks its SU(4) R-symmetry group to a much smaller subgroup, such as SU(2)xU(1) if N=2 supersymmetry is preserved. I will discuss how, by extending our notion of symmetry to include Lie groupoids and their twists, one can recover the broken generators and show that, at the planar level, a version of the full SU(4) symmetry is still present. I will briefly discuss the implications of this hidden symmetry as far as the planar spectrum of the theory is concerned.

14:00-14.30 Speaker: Koji Hashimoto (Kyoto university) Title: "Neural network representation of quantum systems" Abstract: We provide a novel map with which a wide class of quantum mechanical systems can be cast into the form of a neural network with a statistical summation over network parameters. Our simple idea is to use the universal approximation theorem of neural networks to generate arbitrary paths in the Feynman's path integral. The map can be applied to interacting quantum systems / field theories, even away from the Gaussian limit. Our findings bring machine learning closer to the quantum world. The talk is based on a collaboration with Y. Hirono, J. Maeda and J. Totsuka-Yoshinaka, https://arxiv.org/abs/2403.11420 14:30-15:00 Speaker: Akio Tomiya (Tokyo Woman's Christian University) Title: "CASK: A Gauge Covariant Transformer for Lattice Gauge Theory" Abstract: We introduce a Transformer architecture for lattice QCD that is designed to respect the gauge symmetry and the discrete rotational and translational symmetries of the lattice. The core innovation lies in defining the attention matrix via a Frobenius inner product between link variables and extended staples, ensuring gauge covariance. We apply this method to self-learning HMC and find that it surpasses existing gauge covariant neural networks in performance, demonstrating its potential to enhance lattice QCD computations. This talk is based on arXiv:2501.16955.

Symmetry plays an important role in quantum systems: it can constrain the dynamics, give rise to selection rules, and provide computation methods in quantum computers. In recent years there are also new types of symmetries called generalized symmetries discovered in many quantum systems, including non-invertible symmetry and higher group symmetry. These lectures will be about symmetries in various quantum systems and their applications such as constraints on the low energy dynamics. Examples will be discussed in the lectures include quantum mechanics systems, gauge theories, lattice models, and the symmetry includes ordinary and higher form symmetry as well non-invertible symmetry.

Quantum Chromodynamics (QCD) has been a profound source of inspiration for theoretical physics, driving the development of key concepts such as string theory, effective field theories, instantons, anomalies, and lattice gauge theories. In these lectures, I will explore two distinct regimes of QCD - its infrared (IR) and ultraviolet (UV) limits - and the theoretical tools used to study them. In the IR regime, where perturbative techniques break down, Effective Field Theories (EFTs) provide a powerful framework. I will introduce the pion EFT as a tool to study non-linearly realized symmetries and soft theorems. In the UV regime, where QCD becomes amenable to perturbative analysis, I will discuss the Operator Product Expansion and renormalization group equations, focusing on their application to deep inelastic scattering, a cornerstone in the discovery of quarks and gluons. These two regimes illustrate the richness of QCD and its pivotal role in shaping our understanding of fundamental physics.

Topological field theories, or what is otherwise commonly known as topological orders, can be given a rigorous axiomization in terms of higher fusion categories with some extra structure. The extra structure is necessary to incorporate the relevant physical properties of topological orders. With this categorical framework we can give classifications of topological orders in low dimensions. I will explain how this is done for (3+1)d topological orders that are fermionic in nature. with Pedagogical Intro by Juven Wang

Quantum Chromodynamics (QCD) has been a profound source of inspiration for theoretical physics, driving the development of key concepts such as string theory, effective field theories, instantons, anomalies, and lattice gauge theories. In these lectures, I will explore two distinct regimes of QCD - its infrared (IR) and ultraviolet (UV) limits - and the theoretical tools used to study them. In the IR regime, where perturbative techniques break down, Effective Field Theories (EFTs) provide a powerful framework. I will introduce the pion EFT as a tool to study non-linearly realized symmetries and soft theorems. In the UV regime, where QCD becomes amenable to perturbative analysis, I will discuss the Operator Product Expansion and renormalization group equations, focusing on their application to deep inelastic scattering, a cornerstone in the discovery of quarks and gluons. These two regimes illustrate the richness of QCD and its pivotal role in shaping our understanding of fundamental physics.

Quantum Chromodynamics (QCD) has been a profound source of inspiration for theoretical physics, driving the development of key concepts such as string theory, effective field theories, instantons, anomalies, and lattice gauge theories. In these lectures, I will explore two distinct regimes of QCD - its infrared (IR) and ultraviolet (UV) limits - and the theoretical tools used to study them. In the IR regime, where perturbative techniques break down, Effective Field Theories (EFTs) provide a powerful framework. I will introduce the pion EFT as a tool to study non-linearly realized symmetries and soft theorems. In the UV regime, where QCD becomes amenable to perturbative analysis, I will discuss the Operator Product Expansion and renormalization group equations, focusing on their application to deep inelastic scattering, a cornerstone in the discovery of quarks and gluons. These two regimes illustrate the richness of QCD and its pivotal role in shaping our understanding of fundamental physics.

Quantum Chromodynamics (QCD) has been a profound source of inspiration for theoretical physics, driving the development of key concepts such as string theory, effective field theories, instantons, anomalies, and lattice gauge theories. In these lectures, I will explore two distinct regimes of QCD - its infrared (IR) and ultraviolet (UV) limits - and the theoretical tools used to study them. In the IR regime, where perturbative techniques break down, Effective Field Theories (EFTs) provide a powerful framework. I will introduce the pion EFT as a tool to study non-linearly realized symmetries and soft theorems. In the UV regime, where QCD becomes amenable to perturbative analysis, I will discuss the Operator Product Expansion and renormalization group equations, focusing on their application to deep inelastic scattering, a cornerstone in the discovery of quarks and gluons. These two regimes illustrate the richness of QCD and its pivotal role in shaping our understanding of fundamental physics.

This course will give a technical introduction to the black hole information paradox (BHIP). In the first lecture, we will begin with a review of quantum path integrals, both in Lorentzian and in Euclidean signature. We will review the Euclidean path integral connection with statistical mechanics and thermodynamics while also reviewing the derivation of the first law of thermodynamics in standard equilibrium statistical mechanics. We will then introduce the laws of black hole thermodynamics, and study them in particular examples. The second lecture will be devoted to the Unruh effect. We will study free quantum field theory in Rindler space, which, locally, is the spacetime observed by a uniformly accelerated observer. We will derive that this observer measures a temperature related to the observer proper acceleration. The third lecture will be devoted to classical and quantum information theory including notions of conditional probability, mutual information, and entropy inequalities, in settings with finite numbers of degrees of freedom. We will also introduce the Page curve and its significance. Finally, in the fourth lecture we will set up a toy model of the BHIP in Anti de Sitter space (AdS). Because AdS is believed to have a dual description as a conformal quantum field theory, we will use this duality to our advantage. We end with a broad discussion synthesizing what we have learned, and what is left to understand.

This course will give a technical introduction to the black hole information paradox (BHIP). In the first lecture, we will begin with a review of quantum path integrals, both in Lorentzian and in Euclidean signature. We will review the Euclidean path integral connection with statistical mechanics and thermodynamics while also reviewing the derivation of the first law of thermodynamics in standard equilibrium statistical mechanics. We will then introduce the laws of black hole thermodynamics, and study them in particular examples. The second lecture will be devoted to the Unruh effect. We will study free quantum field theory in Rindler space, which, locally, is the spacetime observed by a uniformly accelerated observer. We will derive that this observer measures a temperature related to the observer proper acceleration. The third lecture will be devoted to classical and quantum information theory including notions of conditional probability, mutual information, and entropy inequalities, in settings with finite numbers of degrees of freedom. We will also introduce the Page curve and its significance. Finally, in the fourth lecture we will set up a toy model of the BHIP in Anti de Sitter space (AdS). Because AdS is believed to have a dual description as a conformal quantum field theory, we will use this duality to our advantage. We end with a broad discussion synthesizing what we have learned, and what is left to understand.

This course will give a technical introduction to the black hole information paradox (BHIP). In the first lecture, we will begin with a review of quantum path integrals, both in Lorentzian and in Euclidean signature. We will review the Euclidean path integral connection with statistical mechanics and thermodynamics while also reviewing the derivation of the first law of thermodynamics in standard equilibrium statistical mechanics. We will then introduce the laws of black hole thermodynamics, and study them in particular examples. The second lecture will be devoted to the Unruh effect. We will study free quantum field theory in Rindler space, which, locally, is the spacetime observed by a uniformly accelerated observer. We will derive that this observer measures a temperature related to the observer proper acceleration. The third lecture will be devoted to classical and quantum information theory including notions of conditional probability, mutual information, and entropy inequalities, in settings with finite numbers of degrees of freedom. We will also introduce the Page curve and its significance. Finally, in the fourth lecture we will set up a toy model of the BHIP in Anti de Sitter space (AdS). Because AdS is believed to have a dual description as a conformal quantum field theory, we will use this duality to our advantage. We end with a broad discussion synthesizing what we have learned, and what is left to understand.

Decaying turbulence, characterized by energy dissipation from an initial high-energy state, remains a fundamental challenge in classical physics. This work presents an exact analytical solution to the Navier-Stokes (NS) equations for incompressible fluid flow in the context of decaying turbulence, introducing the novel framework of the \textit{Euler ensemble}. This framework maps turbulent dynamics onto discrete states represented by regular star polygons with rational vertex angles in units of 2π. A key feature of the Euler ensemble is a duality between classical turbulence and a hidden one-dimensional quantum system, analogous to the AdS/CFT correspondence in quantum field theory. This duality enables the derivation of exact turbulence statistics, replacing traditional heuristic scaling laws with universal results derived directly from the NS equations. For example, the decay law for turbulent kinetic energy is predicted as $ E(t)∼t^{−5/4}$, with quantitative agreement to within 1% standard deviation in experimental and numerical data. The framework is validated using Direct Numerical Simulations (DNS) and experimental results, including grid turbulence and large-tank experiments. Additionally, the Euler ensemble predicts novel macroscopic quantum-like effects, such as oscillations in the decay index as a function of the scaling variable $r/\sqrt t$. These predictions highlight new avenues for experimental and numerical exploration of turbulence. This work addresses long-standing challenges in turbulence theory, providing a rigorous, universal description of decaying turbulence with applications across fluid dynamics, geophysics, and engineering.