### Hexagons, Wilson Loops and Q-functions

The hexagonalization procedure arose in the context of AdS/CFT correspondence in order to compute correlation functions in planar N = 4 SYM, a particular corner where the theory is known to become integrable. This approach, formalized by Basso, Vieira and Komatsu in 2015 is based upon a tessellation of the dual closed string worldsheet that permits to obtain two building blocks that can be bootstrapped using the power of integrability. After an introduction about the integrable structures arising in the AdS/CFT correspondence, I will review the hexagonalization technique and how we can suitably modify this procedure in order to compute correlation functions on non-trivial backgrounds such as a Wilson loop and the possible links with other well-known integrability techniques, namely the Q-functions approach and the functional separations of variable (FSoV).

**30 May 2023, 11:00**

### Anomaly constraints on heterotic strings and supergravity

The known string landscape covers a small subset of all consistent-looking effective field theories of (quantum) gravity. A great deal of indications suggest that anything not covered by the landscape is actually inconsistent, usually due to subtle violations of unitarity when quantum gravity effects are at play. The ambitious program of understanding this principle of "string universality" has been quite successful, starting from theories with 32 supercharges and gradually moving down in symmetries and dimensions, but minimal supersymmetry in six dimensions is a prominent roadblock. In this talk I will present some preliminary results in this setting: new anomalies of the Dai-Freed type seem to significantly constrain six dimensional supergravities that would otherwise look consistent, while a large class of heterotic string constructions remain remarkably safe.

**23 May 2023, 14:30**

### Poisson gauge theory

Motivated by noncommutative gauge theory, I will discuss a novel approach to gauge theory with underlying non-trivial Poisson structure over space-time. The goal is to formulate a gauge theory which reproduces the standard one in the 'commutative' limit (e.g. with trivial Poisson bracket) and such that the algebra of gauge parameters closes under Poisson brackets. The case of U(1) gauge theory shall be considered in some detail.

**16 May 2023, 14:30**

### Bounds on photon scattering

We study 2-to-2 scattering amplitudes of massless spin one
particles in four spacetime dimensions, like real world photons. We use
full nonlinear unitarity to construct numerical bounds on the Wilson
coefficients, which describe these amplitudes at low energies. Some of the
bounds can be recovered analytically by using the optical theorem, others
cannot. Finally, some Wilson coefficients cannot be bounded, and we discuss
why.

**09 May 2023, 14:30**

### A bundle geometric perspective on covariant phase space methods for diffeomorphisms symmetry: Applications to gravitational dressings & gravitational edge modes

We emphasise the elementary bundle geometry of the space of fields, F, supporting the action of diffeomorphisms. We first stress that the Lagrangian of a theory with Diff(M) symmetry is a section of a line bundle, associated to F, of a peculiar type: it is a “twisted bundle” generalising the standard notion of associated vector bundle. Then, we sketch how the so-called "dressing field method" allows to build basic forms on F, which then descend as forms on the orbit space F/Diff(M). Finally, we show that it is a unifying framework for gravitational dressings à la Giddings, relational variables à la Rovelli, and gravitational edge modes à la Donnelly-Freidel-Speranza (& others). In the latter case, it allows to systematically build the “extended” covariant phase space of a Diff(M)-theory. We stress the limits of the approach.

**04 May 2023, 14:30**

### Recent advances in precision holography

I will present ongoing efforts to probe the AdS4/CFT3 correspondence beyond the strict large N limit. On the gauge theory side, I will summarize some recent conjectures for the partition functions of 3d SCFTs preserving at least N=2 supersymmetry on various compact Euclidean 3-manifolds. The proposed expressions are perturbatively exact in 1/N, and they are supported by consistency with available analytic results as well as detailed numerical studies. On the gravity side, I will explain how higher-derivative corrections and loop effects account for subleading terms in the large N expansion of boundary observables. Such precision tests of AdS/CFT have important consequences for our understanding of M-theory and quantum aspects of AdS black holes.

**02 May 2023, 14:30**

### The entropy of giant gravitons at large charges

There is strong evidence suggesting a one-to-one correspondence between 1/16 BPS states in U(N) N=4 SYM on S3 and states of Giant graviton D3-branes in AdS5xS5, which extend over three independent contractible S3-cycles in the S5. This correspondence has been verified at small enough charges for small N (N<=3) and for large N (at charges ~N or smaller). The question then arises as to whether this correspondence persists for states with large charges.
In this talk, I will show how this correspondence persists at large charges, regardless of the value of N. In particular, this result completes a recent observation and confirms that the entropy of 1/16 BPS black holes in Type IIB SUGRA in AdS5XS5, with charges of order ~N^2>>1, can be understood as coming from a condensate of giant-gravitons in AdS5XS5.

**18 April 2023, 14:00**

In this talk I will discuss recent developments in the study of 2- and 3-point functions of chiral single-trace scalar operators in four-dimensional N=2 quiver gauge theories. Using supersymmetric localization, it is possible to map the computation of these correlators to an interacting matrix model and obtain expressions that are valid for any value of the ’t Hooft coupling in the planar limit of the theory. In particular, I will focus on the strong-coupling regime, where these expressions allow us to compute the leading and subleading orders of the 3-point functions and of the corresponding structure constants in an analytic way.

**12 April 2023, 14:00**

### 2d Integrable Field Theories from 4d Chern-Simons

In recent years various unifying frameworks for understanding 2d integrable field theories have emerged. In this talk I will review the approach based on 4d Chern-Simons theory, due to Costello and Yamazaki, and describe recent progress towards extracting general 2d integrable fields theories from 4d Chern-Simons theory

**04 April 2023, 14:30**

### Branes and symmetries for N=3 SCFTs

I will explain how to derive various results about the generalised symmetry
structure of N=3 and N=4 S-fold SCFTs using holography. The new results in
the N=3 case include the spectrum of 1-form symmetries, their 't Hooft
anomalies, and the existence of non-invertible symmetries for appropriate
choices of global form.

**28 March 2023, 14:30**