The Landau paradigm of phase transitions states that any continuous (second order) phase transition is a symmetry breaking transition. Originally this was formulated for symmetries that form groups, e.g. the critical Ising model is the transition between the $\mathbb{Z}_2$ symmetric and spontaneously broken phases. In recent years a new class of symmetries, called categorical or non-invertible, have emerged in quantum systems -- with impact ranging from high energy and condensed matter physics to mathematics, and quantum computing. I will explain how these symmetries generalize the Landau paradigm and how new phases and phase transitions are predicted, which have potential future experimental implementations in cold atom systems.

Machine learning and related computational methods have become substantially more powerful and are already applied in many areas of science. In the future, they are likely to change scientific research profoundly. In this talk I will be discussing two ways in which machine learning can be helpful in physics: solving differential equations and model building. I will attempt to explain the basic ideas behind these applications and present some recent examples, including inflationary model building, finding string models with certain prescribed properties and computing the masses of fermions from string theory.

In recent years we've expanded our understanding of entanglement in many-body quantum systems; both how it behaves in ground states, and how it grows out-of-equilibrium. Entanglement is very difficult to measure in experiments. But through understanding it better, we've made great progress in classifying quantum phases of matter, and in developing algorithms for efficiently simulating quantum systems. I will review some recent progress in these directions.

Fundamental questions such as emergence of geometry and gravitational dynamics from QFT amplitudes, barring specific examples, remain unanswered at the full stringy level in gauge-gravity duality. In this talk I will discuss recent progress toward a microscopic approach based on the worldline formulation of QFT. In particular, I will consider large-loop quantum corrections in holographic QFTs where internal propagators of Feynman diagrams are characterized by the Schwinger parameters and argue that embedding of string in the holographic coordinate emerges from the continuum limit of these Schwinger parameters at infinite loop limit. I will demonstrate, employing the techniques of Strebel differentials and discrete exterior calculus, how a worldsheet action for a bosonic string embedded in asymptotically AdS space-time could emerge from multi-loop Feynman graphs in a class of bosonic QFTs. I will end with a discussion of possible loopholes in this approach.

Non-invertible symmetries are refined notions of symmetries intensively studied recently. I will show that non-invertible symmetries sometimes lead to a surprising consequence on scattering amplitudes --- a modification of crossing symmetry. I will demonstrate this using example of integrable field theories in 1+1 dimensions although the argument holds more generally; also for non-integrable theories. I will also present the results of S-matrix bootstrap, which constrains the space of physically consistent scattering amplitudes with categorical symmetries.

SymTFTs (or, relatedly, the sandwich construction) have emerged recently as a useful way to think of categorical symmetries. I will give a brief description of this construction, and then review recent work on how to obtain the SymTFT data from geometry in the context of geometric engineering.

This talk will review recent results on the construction of U(1) duality-invariant nonlinear models for gauge (2n-1)-forms in d = 4n dimensions, including $T \bar T$-like flows in the space of such theories. In the four-dimensional case, we will briefly discuss the following U(1) duality-invariant nonlinear systems: (i) models for N-extended superconformal higher-spin multiplets; (ii) the low-energy effective action for N = 4 SYM on its Coulomb branch; and (iii) models for spontaneously broken local N=1 supersymmetry. If time permits, a new formulation for a self-interacting chiral gauge 2n-form in d = 4n + 2 dimensions will be discussed.

It’s been known since the work of Callan and Rubakov that a generic gauge theory harbours a riddle: the scattering of light fermions off heavy magnetic monopoles necessitates exotic outgoing states, seemingly with fractional occupation numbers. I will first explain how we can make sense of these outgoing states in the modern language of generalised symmetries: They are created by operators living at the edge of a topological surface, and in turn correspond to states in a particular twisted Hilbert space. I will then apply this general formalism to the original case of interest, the Standard Model itself, where the resulting states turn out to carry fractionalised baryon and lepton numbers. I will finally discuss various other scenarios, including some that require non-invertible symmetry defects.

Four-dimensional N=2 superconformal field theories give rise, via a cohomological construction that I will review, to associated vertex operator algebras that have been much investigated in the last decade. A curiosity of this construction is that for unitary parent SCFT, the vertex operator algebras so-realised are non-unitary. In this talk I will present the structure on these VOAs that encodes unitarity of the parent theory. Like conventional unitarity, this hidden unitarity imposes strong constraints. I will describe efforts to impose this constraint for Virasoro VOAs (and possibly affine Kac–Moody vertex algebras) leading to (conjectural) classification results for central charges/levels at which these algebras are compatible with four-dimensional unitarity. The talk is based on work in progress with A. Ardehali, M. Lemos, and L. Rastelli.

We consider type IIB string theory with $N$ D3 branes and various configurations of sevenbranes, such that the string coupling $g_s$ is fixed to a constant finite value. These are the simplest realizations of F-theory, and are holographically dual either to a to a rank $N$ gauge for any coupling tau, or to non-Lagrangian CFTs such as Argyres-Douglas and Minahan-Nemeschansky theory. We compute the mass deformed sphere free energy F(m) using localization in the case of the Lagrangian theory, and the Seiberg-Witten curve for the non-Lagrangian theories. We show how F(m) can be used along with the analytic bootstrap to fix the large N expansion of flavor multiplet correlators in these CFTs, which are dual to scattering of gluons on AdS_5 x S^3, and in the flat space limit determine the effective theory of sevenbranes in F-theory. In particular, we compute the log threshold terms for all the theories and the first higher derivative correction F^4 for the Lagrangian theory for finite tau, and find a precise match in the flat space limit in all cases. Finally, we use numerical bootstrap to study the Lagrangian theory at finite N and tau.

Asymptotically-flat spacetimes play a central role in the study of gravitational radiation. They are also the arena which enables to understand the relationship between asymptotic symmetries, soft graviton theorems, and memory effects. While this relationship is well understood at leading order in terms of BMS symmetries and flux-balance laws for the mass and angular momentum, the subleading structure has only begun to be investigated recently. In this talk we will present a study of this subleading structure using the Newman-Penrose formalism. This enables to identify an infinite tower of quasi-conserved charges generating an intriguing algebraic structure.

Recent progress has provided methods to compute and match finite N (supersymmetric) partition functions on both sides of the holographic duality within string and M-theory. An advent that allows for interesting opportunities in the study of quantized strings and branes in curved backgrounds. I will discuss \mathcal{N}=4 SYM, its S-fold cousins, and how localization allows to compute their supersymmetric partition functions analytically as a function of N. We will subsequently discuss some peculiar features of these S-folds; such as their seemingly non-compact conformal manifold, and the fact that their partition functions can be expanded in fluctuating gravitons and D3-branes, very much a-like the giant graviton expansion in \mathcal{N}=4 SYM, even though a clear index interpretation is absent on the QFT side.

Detecting local Non-Gaussianity provides valuable insights into the early universe's particle composition. Interactions between the inflaton and light particles yield distinctive signatures, potentially observable in upcoming surveys. However, addressing IR divergences in light fields on de Sitter spacetimes requires careful treatment. Stochastic inflation offers a solution, but its relationship with perturbative computations remains unclear. In this presentation, we establish a precise connection between perturbation theory and stochastic formalism using the wavefunction formalism. We extend this analysis to multifield inflation models and clarify recent non-perturbative findings from stochastic inflation through their compatibility with perturbation theory calculations.

I will present a method for deriving the microscopic entropy of a very general class of supersymmetric, rotating, and accelerating black holes in AdS(4). This is achieved by analyzing the large-N limit of the spindle index.

Topological orders in 2+1 dimensions are captured by modular tensor categories (MTCs). We propose a correspondence that assigns a fusion category to a pair (M,G), where M is a Seifert 3-manifold and G is an ADE Lie group. We conjecture that the fusion category associated to (M,G) is an MTC if and only if M has trivial first homology group with coefficients in the center of G. The construction determines the spins of anyons and their S-matrix, and provides a constructive way to access the R- and F-symbols from simple building blocks. We explore the possibility that this correspondence provides an alternative classification of MTCs, which is put to the test by realizing all MTCs (unitary or non-unitary) with rank at most 5.

We describe a powerful new technique for computing various physical observables in supergravity, without solving any supergravity equations. Applications include gravitational free energies, black hole entropies, and central charges and other CFT quantities of interest in holography. In the talk I will aim to describe the general idea, and give a flavour of some applications.

I will review the theoretical and experimental status in the search of primordial non-Gaussianity, focussing on some recent developments and ideas. In particular I will try to answer the question: what are we going to learn when experiments will be able to probe f_NL ~ 1?

Previous work has given proof and evidence that BPS states in local Calabi-Yau 3-folds can be described and counted by exponential networks on the punctured plane, with the help of a suitable non-abelianization map to the mirror curve. This provides an appealing elementary depiction of moduli of special Lagrangian submanifolds, but so far only a handful of examples have been successfully worked out in detail. In this talk, I will present an explicit correspondence between torus fixed points of the Hilbert scheme of points on ℂ^2⊂ℂ^3 and anomaly free exponential networks attached to the quadratically framed pair of pants. This description realizes an interesting, and seemingly novel, “age decomposition” of linear partitions. We also provide further details about the networks’ perspective on the full D-brane moduli space.