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In this talk, I will present irregular representations of Kac-Moody algebras where we restrict ourselves to the sl(2,C) case. I show how such irregular representations correspond to irregular Gaiotto-Teschner representations of the Virasoro algebra. The associated KZ equations for conformal blocks with one irregular operator at infinity and their integral representations are derived. By connecting to 2d Liouville theory, I will show how the conformal blocks governed by our irregular KZ equation correspond to 4d Argyres-Douglas theories with surface operator insertions. The corresponding flat connections describe braiding between such operators on the Gaiotto curve.

We introduce Kolmogorov-Arnold Networks (KANs) as an alternative to standard neural network architectures. KANs are based on Kolmogorov-Arnold representation theory, which means for our purposes that we can represent any function by a weighted sum over basis functions, taken to be splines. While KANs are slower than neural networks of the same size, they have two properties that can offset this cost. First, KANs can typically work with much fewer parameters. Second, they exhibit better neural scaling laws, meaning the error decreases faster when increasing the number of parameters as compared to MLPs. Fewer parameters also mean that KANs are much more interpretable, especially when combined with the sparsification and pruning techniques we introduce. This makes KANs interesting tools in science, as we will illustrate in examples.

What is the full set of observables in quantum gravity? I will introduce and discuss asymptotic detector operators and their measurements in perturbative quantum gravity in asymptotically-flat spacetimes. The simplest example is an energy detector, which detects outgoing graviton radiation and records its energy. I will construct large classes of general detector operators in QFT and in gravity, defined as light-ray operators. I will present the first computation of an energy-energy correlator (EEC) as well as some of its generalizations in perturbative quantum gravity. One can think of such observables as capturing a universal part of quantum correlations between idealized LIGO detectors — as unlikely as it may be to be measured in the real world. Along the way, I will comment on the "space of asymptotic detector operators" in a gravitational theory.

Four-dimensional maximally supersymmetric SU(N) Yang-Mills theory coupled to fundamental representation hypermultiplets is holographically dual to type IIB supergravity in AdS5 x S5 with D7-branes. I will describe a family of D7-brane solutions that correspond to a position-dependent mass for the hypermultiplets, where the mass can be any holomorphic function m(z) of a complex coordinate z. The solutions I describe obey a BPS bound and preserve one quarter of the supersymmetry of the background. I will demonstrate that such position dependent masses trigger a renormalisation group flow that ends at a defect superconformal field theory, with defects located at the zeroes of the mass.

I give an overview of an ongoing research program that aims to give a first-principle derivation of gravity as the "double copy" of gauge theories, such as Yang-Mills theory, using the language of homotopy algebras. In particular, I discuss recent work applying this program to the double copy of N=4 super-Yang-Mills, which yields N=8 Supergravity in a double field theory formulation.

Holography has provided valuable insights into the time evolution of strongly coupled gauge theories in a fixed spacetime. However, this framework is insufficient if this spacetime is dynamical. We present a scheme to evolve a four-dimensional, strongly interacting gauge theory coupled to four-dimensional dynamical gravity in the semiclassical regime. We apply this framework to the description of the gravitational collapse and the subsequent formation of a black hole at the boundary. In the bulk, this corresponds to the formation of a black funnel. If time permits, we will also use holography to study the so-called BKL dynamics near the singularity behind the black hole horizon.

Arithmetic geometry provides a set of novel methods for finding interesting solutions in theories of physics and new techniques for analysing them. In this talk, I concentrate on the example of supersymmetric flux vacua in Calabi-Yau compactifications of string theory. Existence of these vacua requires the Hodge structure of the underlying geometry to satisfy intricate conditions. However, arithmetic methods can be used to replace the required analysis of Hodge structures by the study of factorisations of a set of polynomials.

I discuss in some detail how these factorisations can be related to symmetries of the theory, to properties of the underlying geometry, or to singularities, and how physical quantities are encoded in the arithmetic data. I also comment on some puzzles and ideas raised by the fact that the arithmetic and physical data do not seem to completely coincide. I will illustrate the discussion with an explicit example.

A particularly efficient method for constructing solutions to ten-dimensional or eleven-dimensional supergravity, makes use of lower-dimensional consistent truncations of these higher-dimensional theories, in which the task of solving the field equations is often much easier. 

Useful truncations in this respect are simple gauged supergravities, with a limited field content, whose solutions can all be uplifted to solutions of the parent theory in ten or eleven dimensions, using, for instance, methods of Exceptional Field Theory (ExFT) or Exceptional Generalized Geometry (EGG). A known example is the STU model, whose analytic asymptotically AdS black hole solutions, through the SO(8)-gauged maximal supergravity in D=4,  could be embedded in M-theory and studied within the AdS/CFT correspondence. Similar embeddings of N=2, D=4 models with vector multiplets only, for which analytic black hole solutions are available, into Type IIB theory, were unknown. 

Borrowing methods from ExFT or EGG, we develop a general paradigm for constructing consistent truncations of gauged maximal D=4 supergravities admitting an uplift to Type IIB or D=11 supergravity. Applying this method to a particular gauged maximal supergravity in D=4 it was possible to embed pure N=4 AdS-supergravity, and thus all its solutions, within Type IIB superstring theory. The corresponding ten-dimensional backgrounds are instances of the so-called S-fold solutions and are dual to a special class of three-dimensional interface theories.

The dynamics of linear perturbations of black hole spacetimes are often discussed in terms of quasinormal modes. However, quasinormal modes are eigenfunctions of a non-normal operator, for which the spectral theorem does not apply. I will show that, as a consequence, there are non-modal effects which can lead to large-amplitude growth of linear perturbations in finite time, despite all quasinormal modes decaying exponentially. In the example I will present, the physical mechanism is a transient form of superradiance, which is qualitatively similar to the transition to turbulence in Navier-Stokes shear flows.

Calabi-Yau geometries represent a fascinating class of higher-dimensional varieties that possess intriguing geometric and arithmetic properties. They have traditionally appeared in physics in the context of compactifications of superstring theory. In my talk, I will focus on a relatively new area of application for Calabi-Yau geometries in physics: Precision computations in quantum field theory and general relativity. Even though these two fields of physics look very different at first glance, they share the same underlying mathematical structures, which are period geometries of Calabi-Yau varieties. These structures show up in Feynman integrals, which form the building blocks for calculations in perturbative quantum field theory and the world-line quantum field theory approach to the scattering of black holes in general relativity. During my talk, I will show how to use Calabi-Yau periods and iterated integrals thereof to compute two-point functions in quantum electrodynamics and the 5th post-Minkowskian order. The Feynman integrals involved will be calculated using differential equations that are brought into so-called canonical form with the help of the underlying Calabi-Yau geometry. The form of the derived results allows for efficient numerical evaluations across the required parameter spaces.

The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly by extending differential geometry, such that it can be applied to theories that are non-differentiable, but have a certain degree of Hölder regularity. As this includes the path integral formulation of quantum theory, it provides a natural mathematical framework for describing the interplay between gravity and quantum theory. In this talk, I will review the motivation for and the basic features of this framework and point towards future developments.

There has been much recent interest in the necessity to include an observer degree of freedom in the description of local algebras in semiclassical gravity.  In this talk, I will describe an example where the observer can be constructed intrinsically from the quantum fields.  This construction involves the slow-roll inflation example recently analyzed by Chen and Penington, in which the gauge-invariant gravitational algebra arises from averaging over modular flow in a local patch.  I will relate this procedure to the Connes-Takesaki theory of the flow of weights for type III von Neumann algebras, and further show that the resulting gravitational algebra can naturally be presented as a crossed product.  This leads to a decomposition of the gravitational algebra into quantum field and observer degrees of freedom, with different choice of observer being related to changes in frame for the algebra.  I will also connect this example to other constructions of type II algebras in semiclassical gravity, and argue they all share the feature of being the result of gauging modular flow.  

Thin enough black strings are unstable to growing ripples along their length, eventually pinching and forming a naked singularity on the horizon. We investigate how string theory can resolve this singularity. First, we study the string-scale version of the static non-uniform black strings that branch off at the instability threshold: “string-ball strings”, which are linearly extended, self-gravitating configurations of string balls obtained in the Horowitz-Polchinski (HP) approach to near-Hagedorn string states. We construct non-uniform HP strings in spatial dimensions d ≤ 6 and show that, as the inhomogeneity increases, they approach localized HP balls. We also examine the thermodynamic properties of the different phases in the canonical and microcanonical ensembles. We find that, for a sufficiently small mass, the uniform HP string will be stable and not evolve into a non-uniform or localized configuration. Building on these results and independent evidence from the evolution of the black string instability with α' corrections, we propose that, at least in d = 4, 5, string theory slows and eventually halts the pinching evolution at a classically stable stringy neck. In d ≥ 6 this transition is likely to occur into a puffed-up string ball. The system then enters a slower phase in which the neck gradually evaporates into radiation. We discuss this scenario as a framework for understanding how string theory resolves the formation of naked singularities.

Higgs branches in theories with 8 supercharges change as one tunes the gauge coupling to critical values. This talk will focus on six dimensional (0,1) supersymmetric theories in studying the different phenomena associated with such a change. Based on a Type IIA brane system, involving NS5 branes, D6 branes and D8 branes, one can derive a "magnetic quiver” which enables the construction of the Higgs branch using a “magnetic construction” or as a more commonly known (but misnamed) object “3d N=4 Coulomb branch”. Interestingly enough, the magnetic construction opens a window to a new set of Higgs branches which were not available using the well studied method of hyperkahler quotient. It turns out that exceptional global symmetries are fairly common in the magnetic construction, and few examples will be shown. In all such cases there are strongly coupled theories where Lagrangian description fails, and the magnetic construction is helpful in finding properties of the theory. Each Higgs branch can be characterized by a phase diagram which describes the different sets of massless fields around vacua. We will use such diagrams to study how Higgs branches change. If time permits we will show an interesting exceptional sequence consisting of SU(3), G2, and  SO(7). 

Recently, symmetries have been reinterpreted in terms of topological operators supported on codimension 1 submanifolds of spacetime and satisfying group-like and invertible fusion rules. This has naturally led to the notion of generalized symmetries as categories of topological defects supported on arbitrary codimension submanifolds with possibly non-invertible fusion rules. In this talk, I will present first results toward the classification of topological defects that commute with the spectral flow and the N = (4,4) superconformal symmetry in two dimensional non-linear sigma models on K3, as well as those that preserve supersymmetry in the Conway superconformal field theory V f♮. By analyzing the induced action of these defects on the lattice of RR D-brane charges in the K3 models, and on a particular embedding of the Leech lattice into the space of Ramond ground states in the Conway theory, I will extract a number of parallel structural results for the respective categories of topological defects.

These findings lead me to conjecture a correspondence between four-plane-preserving topological defect lines (TDLs) in V f♮ and supersymmetry-preserving TDLs in K3 non-linear sigma models. This correspondence extends the known relation between the symmetry groups of the two theories to a deeper equivalence at the level of their tensor categorical symmetries.

Some fundamental theories predict the existence of magnetically charged objects. These may be gravitationally compact—such as magnetic black holes or magnetic, horizonless geometries—and their gravitational signatures could offer new ways to probe their existence. In this talk, I will show that energy extraction from magnetic black holes proceeds in a fundamentally different manner than in their neutral or electrically charged counterparts. Specifically, they are unstable to growing charged matter clouds that extend along the rotational axis—rather than the equatorial plane—resulting in both gravitational and electromagnetic radiation.

I will also explore what happens when the black hole is replaced by a horizonless, magnetically charged microstate geometry—commonly referred to as a topological star. In this scenario, I will demonstrate that the star can support long-lived bound states of matter in its vicinity, whose only decay mechanism is via sustained emission of gravitational and electromagnetic radiation at specific, quantised frequencies.

I will conclude by discussing potential phenomenological implications of these findings, along with some future research directions.

In this talk, I will present a class of completely regular charged black hole solutions in three dimensions, as introduced in [arXiv:2104.10172 [gr-qc]]. These solutions are free of singularities without requiring any fine-tuning of the theory's parameters or the black hole's physical charges. I will outline the underlying mechanism responsible for this regularity and explore the internal structure of these black holes from three different perspectives: their Penrose diagrams, the geodesics of probe particles, and the transitions among effective Kasner exponents characterizing the spacetime dynamics in the interior region. The talk will be based mainly on [arXiv:2503.02930 [gr-qc]].

In this talk I will discuss a new constructive approach for classifying and finding integrable models. By using our method we have found new integrable models in fields ranging from string theory to condensed matter systems. I will discuss some of our new models and applications to for example AdS/CFT.

I will describe how to consider the flat space limit of scattering in AdS relative to a point (where scattering occurs). The kinematics is related to the Wigner-Inonu contraction. In particular, I will discuss how to take the proper limits of wave functions in AdS (times extra dimensions) to understand a notion of in states and out states and how a scattering amplitude should be conceived.  This will make use of the embedding formalism, where the description of these wave functions is simple. I will show how these wave functions are related to other constructions in AdS/CFT and suggest how the Mellin parameters of these other setups arise from integral representations of the wave functions in terms of Schwinger parameters.

Whether flux compactifications can feature scale separation, i.e. cosmological constant can be much smaller than the KK mass scale, is an important and still debated issue. In this talk, I will provide evidence for the existence of such scale-separated, supersymmetric AdS4 vacua in M-theory of the Freund-Rubin type. The internal space has weak G2-holonomy, which is obtained from the lift of AdS vacua in massless type IIA on a specific SU(3)-structure with O6-planes. Such lifts require a local treatment of the O6-planes, therefore going beyond the usual smeared approximation. I will show how this can be achieved while preserving supersymmetry manifestly, extending on previous work.

We will review the classical double copy, which maps exact solutions of classical gauge theories like electromagnetism, to solutions of general relativity. We will cover both the Kerr-Schild and Weyl formulations of this map.  Following a survey of known exact solutions, we will review why a position-space classical solution double copy is even feasible.  We will briefly discuss some perturbative approaches, and then close by relating several gravitational objects (including horizons and Penrose limits) to their gauge theory analogues.

I will discuss the evidence for a spatially modulated instability within the deconfined quark-gluon plasma phase of QCD. This evidence is based on robust predictions from generic bottom-up holographic models, which have been accurately fitted to lattice data. The instability, known as the Nakamura-Ooguri-Park instability, is driven by the Chern-Simons term mandated by QCD flavor anomalies. Contrary to common expectations, this instability occurs universally across holographic models at surprisingly low densities and high temperatures, within the crossover region accessible to lattice and experimental studies. However, the precise extent of the instability region remains sensitive to flavor dependence which is not yet incorporated in current models.

Hydrodynamics is a cornerstone of physics. Formulated initially to describe the flow of water, it has since been successfully applied to model the collective motion of various systems at vastly different length scales, ranging from cosmological distances to the size of an atomic nucleus. In the hydrodynamic description, microscopic and quantum details of specific systems are "averaged over," producing an effective classical theory. Yet, we know that the physical world consists of interacting particles exhibiting inherent quantum properties. Thus, it is natural to ask how such collective behavior emerges from the underlying quantum theory and whether there are scenarios where quantum effects become amplified, influencing macroscopic hydrodynamic processes. In this talk, I will discuss the latest developments in the formulation of relativistic hydrodynamics with spin and quantum anomalies. I will focus on applications to the physics of the quark-gluon plasma, a relativistic quantum fluid created in heavy-ion collisions, which is also believed to have filled the Universe a few microseconds after the Big Bang.

One of the main challenges for string theory phenomenology is to reliable identify consistent four-dimensional vacua of string theory with low or broken supersymmetry. This task is difficult as one expects no such vacua in the asymptotic limits where one sends all coupling constants to zero or (equivalently) all moduli fields to infinity. On the other hand, once these fields take finite values there exist various quantum and string corrections to the low-energy effective action that are difficult to compute and often unknown.

In this talk I will propose an index formulation based on contour integration techniques that relates the existence of critical points of effective potentials to their behaviour at the asymptotic boundaries of the field space. I will demonstrate this technique and discuss possible challenges for the specific example of IIB / M-theory flux compactifications with a one-dimensional complex structure moduli space and the resulting N=1 supersymmetric F-term potential.

In the context of inflationary cosmology a natural question arises on what precedes inflation itself. We review aspects of the Hartle-Hawking (no boundary) and Vilenkin (tunneling) proposals, and their relation to the Wheeler-DeWitt equation. These raise some paradoxes that are complementary in nature and in clash with observations. On the other hand theories of quantum gravity are better defined in the presence of a negative cosmological constant. I will propose a new type of wavefunction of the universe with asymptotically AdS boundary conditions in the far (Euclidean) past. In the semiclassical limit, it describes a Euclidean (half)-wormhole geometry with properties that result in an expanding universe upon analytic continuation to Lorentzian signature. In this context some of the aforementioned phenomenological issues can be resolved.  

I will give an overview of a very rich worldsheet string theory obtained by coupling two Liouville theories with complex central charges. This worldsheet theory enjoys a duality with a double scaled matrix integral and can be used to probe many aspects of string theory and quantum gravity: It can be completely solved from the worldsheet by an analytic bootstrap approach, which effectively consistutes a first principle derivation of the duality with the matrix model. It can also be used to study observables with boundaries in string theory and is a simple laboratory to explore non-perturbative effects in string theory. It is classically equivalent to a theory of dilaton gravity on the worldsheet with a sine potential, which exhibits infinitely many vacua, both with positive and negative cosmological constant and thus provides a rigorous window into the study of such theories. Finally, it can be related to cosmological correlators in dS3 where the matrix model provides a microscopic realization of dS3.

Interacting quantum field theories typically thermalize, leading to the emergence of hydrodynamics at late times. I will talk about (1+1)d QFTs at high and low temperatures, where the proximity to a CFT results in parametrically slow thermalization, with much of the associated dynamics tractable. I will first explain how the UV effective theory – conformal perturbation theory – breaks down universally at late times due to the unsuppressed exchange of stress tensors, giving room for hydrodynamics to emerge. Specialising to the case of large central charge, I will then argue that the IR effective theory – hydrodynamics -- has universal transport coefficients and use this to show that it breaks down at early times due to the existence of thermal CFT excitations. The timescales at which the two effective theories break down agree.

13h30: Tea & Coffee.
14h00: Speaker 1: Andrei Parnachev (Dublin), “Operator product expansion, geodesics and black hole singularities”
15h15: Coffee break.
15h45: Speaker 2: Nabil Iqbal (Durham/UvA),  “Machine learning approach to duality in statistical physics”
17h00: Borrel (drinks and snacks): Cafe Minnaert
 

Compared to their counterparts with enhanced supersymmetry, little is known about the field spaces of theories of gravity with minimal supersymmetry in four dimensions away from asymptotic weak coupling limits. In this talk, I will focus on 4d N=1 theories obtained as compactifications of the heterotic string on Calabi-Yau threefolds and investigate the interior of its field space. In particular, I will focus on certain strong coupling singularities for the heterotic gauge group that arise at the perturbative level and naively cap off the moduli space at finite distance. In the dual M-theory compactification on a Calabi-Yau threefold times an interval the perturbative strong coupling singularity of the heterotic string manifests itself as an end-of-the-world domain wall. In this dual setup, I will discuss the fate of the strong coupling singularity at the non-perturbative level by studying the instanton corrections to the BPS equations of the domain wall which are inherited from the 5d N=1 parent theory. I will argue that these instanton corrections effectively resolve the end-of-the-world singularity of the domain solution which translates into a resolution of the original strong coupling singularity of the heterotic string. 

A notion of distance on the moduli space of low-energy effective field theories is crucial for the Swampland program, and specifically for the Distance Conjecture. In this talk, I will show how geometric flow equations, and in particular generalizations of the Ricci flow, offer a different and elegant viewpoint in the more general case of a scalar field space with potential. After a brief introduction to Ricci flow and its generalization to backgrounds involving a NSNS two-form, I will review the known realization as a gradient flow of the string-effective action and the associated beta-functions, ultimately proposing a suitable notion of distance along the flow as well as a generalized Ricci flow Conjecture. I will discuss examples highlighting the new and intriguing implications as well as the connection to previous work on the role of (diverging) potentials. 

This work is in collaboration with Saskia Demulder and Dieter Lüst.