Join here (you need Microsoft Teams). Typical systems of many particles in strong interaction have extremely complex behaviours which are hard to study in detail. But when the system is very large, simplicity resurfaces: typically just a few degrees of freedom are relevant, which follow new, simple laws. Understanding what the emergent behaviours are from the underlying microscopic interactions is one of the foremost problems in modern science. A very powerful set of ideas and tools at our disposal is hydrodynamics. Although the Navier-Stokes and related equations have been studied for a very long time, we are now starting to uncover the full potential of the fundamental principles of hydrodynamics. In particular, in a recent breakthrough it was understood how to apply these principles to quantum and classical integrable models, where infinitely many conserved currents exist, giving ``generalised hydrodynamics”. I will overview the fundamental principles of hydrodynamics and their adaptation to integrable systems, with simple examples such as the quantum Lieb-Liniger model, the classical Toda model, and the soliton gases. I will discuss a recent cold-atom experiment that confirmed generalised hydrodynamics, and, if time permits, show some of the exact results that can be obtained with this formalism, such as exact nonequilibrium steady states and exact asymptotic of correlation functions at large space-time separations.

We propose a unified description of two important phenomena: color confinement in large-$N$ gauge theory, and Bose-Einstein condensation (BEC). The key lies in relating standard criteria, based on off-diagonal long range order (ODLRO) for BEC and the Polyakov loop for gauge theory: the constant offset of the distribution of the phases of the Polyakov loop corresponds to ODLRO. Indistinguishability associated with the symmetry group --- SU(N) or O(N) in gauge theory, and S_N permutations in the system of identical bosons --- is crucial in either case. This viewpoint may have implications for confinement at finite N, and for quantum gravity via gauge/gravity duality. As a byproduct, we obtain a characterization of the partially-confined/partially-deconfined phase at finite coupling: the constant offset of the distribution of the phases of the Polyakov loop is the order parameter.

I will review the relation between symmetries and charges and explain how this works in the context of gravity. I will then explain how dual charges can be derived from a similar procedure.

The principles of Lorentz invariance, locality and unitarity highly constrain the physics at accessible high energy: the type of interactions allowed as well as most of the theorems known in particle physics are instances of these principles. This is neatly seen in the structure of scattering amplitudes in asymptotically flat space-times. However, cosmology suggests that such principles may be just approximate: Lorentz invariance is broken at cosmological scales and the accelerated expansion of the universe seems to prevent a full-fledge definition of quantum mechanical observables. If our fundamental ideas in particle physics become somehow approximate in cosmology, what are the fundamental rules governing cosmological processes? In this talk I will report on a recent program which aims to address this question, by bringing both philosophy and methods which have been successful for scattering amplitudes to the analysis of cosmological observables. In particular we investigate the analytic properties of the perturbative wavefunction of the universe, how fundamental physics is encoded into it, how the flat-space physics reflects into it, and how all these features are encoded into new mathematical structures, which can be used as a novel first principle definition of the perturbative wavefunction.

In this talk I will explore the space of two-to-two S-matrices in two-dimensional theories with a global O(N) symmetry, as restricted by the general principles of unitarity, crossing and analyticity. I will describe various features of the allowed space and identify some special points on its boundary with known integrable theories. Finally, I will present a useful dual formulation of the S-matrix bootstrap problem. Based on arXiv:1909.06495.

The correlation functions (three and higher point) in N=4 SYM can be computed using integrability techniques. One formalism is called hexagonalization and its main object is an integrable form-factor with hexagonal shape. It was successfully used to compute a specific all loop four-point function for the first time. However, it seems that new developments are needed to understand the five-point function and other kinds of finite size corrections. In this talk, after a long review of the hexagonalization procedure, I will explain the five-point calculation at weak coupling and its difficulties.

Finding a theoretical framework to explain how phenomenological transport laws on macroscopic scales emerge from microscopic deterministic dynamics poses one of the most significant challenges of condensed matter physics. In recent years, the advent of the generalized hydrodynamics in integrable quantum systems and more recent studies of quantum chaos and its relation to transport, reinvigorated the field of nonequilibrium physics in spin chains. Numerous results were found: lower bounds to diffusion constants, exact expressions for diffusion coefficients and remarkable anomalous features of transport in quantum and classical chains, deeply related to the Kardar-Parisi-Zhang dynamical universality class. I will present an overview of such results with a particular focus on anomalous transport and its relation to non-linear hydrodynamics.

TBA

In this talk I will present the novel developments pertaining the the thermodynamics of the XXZ spin-1/2 chain. I will describe the analysis allowing one to prove several features related to the behaviour of the Heisenberg-Ising (or XXZ) spin-1/2 chain at finite temperature. It has been argued in the literature that the per-site free energy or the correlation length admit integral representations whose integrands are expressed in terms of solutions of non-linear integral equations. The derivations of such representations rested on various unproven conjectures such as the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the existence and uniqueness of the solutions to the auxiliary non-linear integral equations in the infinite Trotter limit. I will show how these conjectures can be proven in a rigorous setting for temperatures high enough. The result of these analyses allowed one to observe that a subset of sub-dominant Eigenvalues of the quantum transfer matrix admits a large temperature asymptotic expansion.

I will review asymptotic charges in electromagnetism and explain why they are physical. Then I will review BMS charges in asymptotically flat spacetimes and show that there are in fact magnetic analogues of BMS charges that had been overlooked in the literature. I will comment on the implications of these newly found charges.

Since the 1980s, the study of invariants of 3-dimensional manifolds has benefited from the connections between topology, physics and number theory. Recently, a new topological invariant has been discovered: the homological block (also known as the half-index of certain 3d N=2 theories). When the 3-manifold is a Seifert manifold given by a negative-definite plumbing the homological block turned out to be related to false theta functions and characters of logarithmic VOA's. In this talk I describe the role of quantum modular forms, false and mock theta functions in the study of the topology of 3-manifolds. The talk is based on the article 1809.10148 and work in progress with Cheng, Chun, Feigin, Gukov, and Harrison.

In this talk, we discuss conformal field theories in two dimensions (2d CFTs) and aspects of the theory of modular forms. Physical considerations lead us to study two extensions to the theory of modular forms: modular forms for GL2(Z) that are defined on the double half-plane (in distinction to SL2(Z) modular forms defined on the upper half-plane), and L-functions for modular forms with poles *within* the fundamental domain. We introduce both concepts, and discuss their consistency, both with each other and with the physical considerations which led to them. Finally, we note that very similar physical considerations may apply to finite-temperature path integrals for generic QFTs in higher dimensions, and comment on possible consequences of this.

Novel insights into quantum gravity in asymptotically flat spacetimes evolving around soft theorems in scattering amplitudes, memory effects and asymptotic symmetries hint at an underlying holographic structure of Minkowski spacetime: information about 4D quantum gravity might be encoded in a 2D CFT on the celestial sphere at the conformal boundary of Minkowski spacetime. I will discuss recent progress on this attempted formulation of a flat space holography focusing on the 4D S-matrix which takes the form of a 2D correlator on the celestial sphere in a conformal basis. I will discuss how celestial conformal symmetry is generated by "conformally soft" gravitons and how insertions of the BMS supertranslation current in a correlator gives rise to the celestial analogue of Weinberg's soft graviton theorem.

Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles'' of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and nonlinear optical media these ``integrable'' gases present fundamental interest for nonlinear physics. We develop nonlinear spectral theory of breather and soliton gases by considering a special, thermodynamic type limit of the nonlinear dispersion relations for multi-phase (finite-gap) solutions of the focusing nonlinear Schrödinger (fNLS) equation. A number of concrete examples of breather and soliton gases are considered, demonstrating efficacy of the developed general theory and also having some interesting implications. In particular, the statistical properties of a special kind of soliton gas, that we term the bound state soliton condensate, reveal a remarkable connection with the nonlinear stage of modulational instability. This is joint work with Alex Tovbis (Central Florida).

I will review recent progress in our understanding of light-ray operators in abstract CFTs. Light-ray operators first appeared in QCD and were later studied in N=4 Super Yang-Mills theory and holography by Hofman and Maldacena. More recently, they attracted new interest due to an important role played by the averaged null energy condition (ANEC) operator in various contexts. However, it is only during the last few years it became possible to start developing a more general theory of light-ray operators. I will explain a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. I will discuss its application to energy-energy correlators in N=4 Super Yang-Mills theory.

Certain quantum field theories possess generalized global symmetries; just as ordinary global symmetries enforce the conversation of particle number, generalized global symmetries enforce the conservation of extended objects, such as strings. I will review this symmetry principle and argue that it governs the long-distance physics of conventional 4d electromagnetism, where the strings in question are magnetic field lines. I will then apply it to construct a novel effective theory for the description of strongly magnetized plasmas. One potential application of this new effective theory is to astrophysical pulsars, which are thought to be surrounded by strong magnetic fields as well as a high density of charged particles; the resulting zero temperature system is highly nonlinear. At leading order in derivatives our new effective theory agrees with the standard treatment in terms of ``force-free electrodynamics''. The inclusion of higher derivative terms however generically results in new and potentially observationally relevant effects, such as electric fields that accelerate charges to high energies along magnetic field lines. If time permits I will describe some recent work towards describing such energetic charges in terms of bosonization along magnetic field lines.

In this talk, I will describe new mathematical structures in the low-energy expansion of one-loop string amplitudes. The insertion of external states on the open- and closed-string worldsheets requires integration over punctures on a cylinder boundary and a torus, respectively. Suitable bases of such integrals will be shown to obey simple first-order differential equations in the modular parameter of the surface. These differential equations will be exploited to perform the integrals order by order in the inverse string tension, similar to modern strategies for dimensionally regulated Feynman integrals. Our method manifests the appearance of iterated integrals over holomorphic Eisenstein series in the low-energy expansion. Moreover, infinite families of Laplace equations can be generated for the modular forms in closed-string low-energy expansions.

I discuss the dependence of supersymmetric partition functions on continuous parameters for the flavour symmetry group. In the presence of the 't Hooft anomalies, the supersymmetric Ward identities imply that the partition function computed in the Wess-Zumino gauge has a non-holomorphic dependence on the flavour parameters. I show this explicitly for a large class of 4d N=1 partition functions on half-BPS four manifolds. I propose a new expression for the partition functions on M3 x S1, which differs from earlier holomorphic results by a non-holomorphic Casimir pre-factor.

Costello, Witten, and Yamazaki have recently proposed a new description of quantum integrable systems using a variant of Chern-Simons theory defined on the product of a two dimensional real manifold and a Riemann surface. I'll review their work, and show how to extend it to describe integrable systems with boundary. In particular I'll discuss how it can be used to generate solutions of the boundary Yang-Baxter equation, and how to realise twisted Yangians in the theory. If there is enough time I will explore the result of applying this construction when the Riemann surface is chosen to be a torus.

A large class of 4d SCFTs can be engineered by wrapping a stack of M5-branes on a compact space, possibly with defects. ‘t Hooft anomalies are crucial observables for such theories, which often do not admit any known Lagrangian description. Building on the seminal work of Freed, Harvey, Minasian, Moore, we develop systematic tools for extracting the ‘t Hooft anomalies of a geometrically engineered 4d theory using anomaly inflow from the M-theory bulk. We exemplify our tools by studying a class of setups with M5-branes probing a C^2/Z_2 singularity. We argue that these setups define 4d SCFTs which are dual to a class of AdS_5 solutions­—first discussed by Gauntlett, Martelli, Sparks, Waldram—whose field theory interpretation has been a longstanding puzzle.