Abstract
Perturbation theory remains the most general approach to understanding generic quantum theories. However, the series obtained in this way are usually divergent and need to be complemented by additional, non-perturbative information. The theory of resurgence is a framework to make sense of divergent series by using resummation techniques and including non-perturbative information in the form of “trans-series". In quantum mechanics, many observables can be fully understood by using the theory of resurgence, but quantum field theories are more challenging. In realistic quantum field theories, the main source of non-perturbative corrections to the perturbative series are the so-called renormalons, which remain mysterious objects. In this talk I will present the basics of the theory of resurgence and some successful applications in quantum mechanics. I will then move to quantum field theories. In order to address the problems due to renormalons, I will focus on integrable, asymptotically free theories in two dimensions where one can make very explicit analysis. I will show in concrete examples that observables can be computed by trans-series due to renormalons, and I will discuss more generally the virtues and limits of the resurgent approach.

Abstract
Is it possible to derive non-perturbative contributions in a quantum field theory knowing only the perturbative coefficients? We answer this question affirmatively based on the careful analysis of the integrable two dimensional O(4) sigma model. We investigate its ground state energy in a magnetic field, for which integrability provides an exact linear integral equation. By cleverly expanding this equation we could calculate a large number of very precise, factorially growing perturbative coefficients. By investigating their asymptotical behaviour on the Borel plane we managed to reveal a nice resurgence structure leading to the first few exponentially suppressed non-perturbative terms of the ambiguity free trans-series. We checked our results against the direct numerical solution of the exact integral equation and find complete agreement. (based on 2011.12254 and 2011.09897)

Abstract
I will revisit the Seiberg-Witten description of the Coulomb branch of rank-one 4d N=2 supersymmetric QFTs, including aspects of the global symmetry, from the point of view of rational elliptic surfaces. This will include, in particular, a detailed study of the 5d superconformal field theories with E_n symmetry, compactified on a circle. I will also sketch how to derive BPS quivers from that perspective. Interesting modular properties of the SW geometries will play a key role.

Abstract
It has long been speculated that a black hole in string theory turns into highly excited strings close to the Hagedorn temperature. Gravitational attraction pulls different parts of the string together, forming a star-like configuration. In this talk, I will review the properties of a concrete solution of this kind, first discovered by Horowitz and Polchinski. I will discuss whether the Horowitz-Polchinski solution can be smoothly connected with the black hole as worldsheet CFTs. I will also discuss how the story can be generalized to charged cases, as well as its implication on the near extremal limit.

Abstract
Simple, local operators irreversibly grow into ones with higher complexity at late times in quantum chaotic systems. In this talk, I shall discuss this dynamics of operator growth in irrational 2d CFTs. First, I shall review a recent paradigm, based on the Lanczos algorithm, to analyze operator growth in quantum systems. I shall then demonstrate how this algorithm can be suitably modified for 2d CFTs and how to extract quantitative features regarding growth of simple operators (primaries and the stress tensor). Under a specific evolution protocol, growth of primary operators proceeds as a flow into the 'bath of descendants' of its Verma module. These descendants are labeled by integer partitions and have a one-to-one map to Young diagrams. This correspondence leads to a concrete visualization of operator growth as paths spreading along the Young's lattice. (Based on arXiv:2110.10519 with Pawel Caputa)

Abstract
The spectrum of BPS states of M theory on local del Pezzo and Hirzebruch surfaces encodes rank-zero DT invariants for the associated derived category of coherent sheaves. Combining wall-crossing invariance with affine Lie symmetries realized as automorphisms of the BPS quiver, we derive exact constraints on the BPS monodromy of Kontsevich-Soibelman. Solving these equations leads to conjectural expressions for the BPS monodromy, encoding the whole BPS/DT spectrum in any chamber of the moduli space of stability conditions. Based on joint work with Fabrizio del Monte.

Abstract
I will argue that the TTbar deformation of a field theory may be understood as a coupling to an elastic medium, with, however, unusual properties. In the fixed stress ensemble the evolution equations are then much simpler compared to the usual fixed geometry, and are explicitly modular invariant. In fact they are those of a simple fluid, for which, however, the singular initial conditions of conformal field theory may lead to the formation either of shock waves, or collapse, giving rise to the observed singular behavior of the partition function in fixed geometry.

Abstract
I will discuss 2-group symmetries in 5d and 6d theories, with a particular focus on superconformal field theories (SCFTs). These symmetries arise when the discrete 1-form symmetry and continuous flavor symmetry group of a theory mix with each other under group multiplication. I will first introduce some general aspects about 2-groups. I will then describe how the 2-group symmetry appears in a specific locus of the extended Coulomb branch of the 5d N=1 SU(2) theory at 0 theta angle. More examples of 2-groups in 5d will be provided, where a notion of perturbative and non-perturbative 2-group can be introduced. Finally, I will discuss the classification of 6d theories with 2-group symmetries.

Abstract
Celestial amplitudes reveal two-dimensional conformal properties of scattering amplitudes for massless particles. In this talk we describe the factorization properties of infrared regulated gluon amplitudes in terms of celestial data. We show that the full divergent contribution becomes a scalar correlator of the product of celestial primaries. The effect of these operators on the hard amplitude is a shift in the scaling dimensions of each asymptotic state by an infinite amount, proportional to the cusp anomalous dimension. We finalize this talk by commenting on the properties of the celestial CFT controlling infrared and non-abelian degrees of freedom.

Abstract
The BMS (Bondi-van der Burg-Metzner-Sachs) symmetry arises as the asymptotic symmetry of flat spacetime at null infinity, suggesting a holographic duality between Einstein gravity and some quantum field theory with BMS invariance. In particular, the BMS algebra in three dimensions is generated by super-rotation generators which form a Virasoro sub-algebra, together with mutually-commuting super-translation generators. In this talk, I will first review flat holography in three dimensions, and then describe a free scalar model in two dimensions exhibiting BMS symmetry.

Abstract
We will discuss what the p-adic tensor network may have taught us about RG fixed point and how those ideas can be generalized to 1+1 dimensional CFTs and beyond, making use of the connection between CFTs and topological theories in one higher dimensions.