### Quantum Spacetime, Noncommutative Geometry and Quantum Observers

Since the dynamical variable of general relativity is spacetime itself, it is natural to think that a quantization of gravity requires a quantization of spacetime, possibly described by a noncommutative geometry. Such a quantum spacetime requires quantum symmetries, and a quantization of observers/references frames. I will introduce the necessity for a quantum spacetime, and describe some instances for which symmetries and observers are likewise quantized.

**20th February 2024, 14:30**

### Quantized Strings and Instantons in Holography

I will present two examples where we compute worldsheet instanton contributions to holographic observables in type IIA string theory. In the first case, the string lives in a ten-dimensional background geometrically realized by spherical D4-branes and dual to maximally supersymmetric Yang-Mills on a five-dimensional sphere. In the second example the background is AdS4 x CP3, which is dual to ABJM in the type IIA limit. Our computations match non-perturbative corrections to the dual field theory free energy obtained via supersymmetric localization. If time allows, I will also discuss the extension of such analysis to semiclassical M2 brane partition functions in eleven-dimensional backgrounds, and their field theory duals.

**13 February 2024, 14:00**

### Bootstrapping the Long-Range Ising model

We combine perturbation theory with analytic and numerical bootstrap techniques to study the critical point of the long-range Ising (LRI) model in two and three dimensions. This model can be interpreted as a conformal defect in an auxiliary, free scalar bulk CFT. We explain how this interpretation can be used in order to gain non-perturbative information on the critical behaviour of LRI. When we combine these approaches within the numerical bootstrap. We find a family of sharp kinks for two- and three-dimensional theories which compare favourably to perturbative predictions, as well as some Monte Carlo simulations for the two-dimensional LRI. (Based on 2311.02742.)

**7 February 2024, 14:00**

I will discuss a connection between harmonic analysis on hyperbolic n-manifolds and conformal field theory in n-1 dimensions. Used in one direction, this connection leads to new spectral bounds on hyperbolic manifolds. Used in the other direction, it offers a new viewpoint on the spectral data of conformal field theories.

**30 January 2024, 14:00**

### Low d singularities

We study black holes in two and three dimensions that have spacelike curvature singularities behind horizons. The 2D solutions are obtained by dimensionally reducing certain 3D black holes, known as quantum BTZ solutions. Furthermore, we identify the corresponding dilaton potential and show how it can arise from a higher-dimensional theory. Finally, we show that the rotating BTZ black hole develops a singular inner horizon once quantum effects are properly accounted for, thereby solidifying strong cosmic censorship for all known cases.

**23 January 2024, 14:00**

### The Regge bootstrap for weakly coupled dual model amplitudes

Dual models describe the tree-level exchange of infinitely many higher spin resonances, as in tree-level string theory and large N gauge theories. They are the simplest non-trivial scattering amplitudes that one can hope to build explicitly. Yet, numerically bootstrapping them has proven extremely difficult, in part because of the slow convergence of their expressions as infinite sums.
In this talk I will present a numerical linear programming bootstrap to construct dual model amplitudes from the data of their Regge trajectories. The bootstrap method relies on an efficient parametrization of the amplitude in terms of Mandelstam-Regge poles, and a thorough understanding of the analytical structure of this expansion in the complex plane.
After introducing some basic notions on Regge theory and explaining the method, I will show some first results obtained with it: Firstly I will explain how it is possible to "rediscover" the Veneziano amplitude within this framework by constraining our ansatz for the amplitude to a restricted parameter space, and then I will use the lessons learned from this exercise to investigate a toy-model deformation with bending trajectories mimicking some features of QCD.

**16 January 2024, 14:00**

In this talk I will present a few conjectures on the transcendental weight of certain two-point functions of local operators in N=4 SYM, at perturbative level. I will also describe a three-loop calculation of structure constants in N=4 SYM with two spinning operators, which inspired those conjectures.

**09 January 2024, 14:00**

### Degeneration, Geometry and Duality

**19 December 2023, 14:00**

### Thermodynamics of near-extreme Kerr

Black holes have been celebrated as "the Hydrogen Atom of the 21st century". From the perspective of classical gravity, a black hole is the simplest object we know of. At the same time, it possesses huge entropy, hinting at an incredibly complex microstructure: understanding this complexity falls in the realm of quantum gravity. In this talk I will review recent results concerning the microscopics and the thermodynamics of black holes, especially in the context of holography. I will focus in particular on the thermodynamics of the fast spinning black holes, and I will describe how recently developed techniques (in collaboration with D. Kapec, A. Sheta and A. Strominger) allowed to compute the quantum corrections to the entropy of near-extremal Kerr black holes, resolving some of the long-standing puzzles concerning the low temperature limit of black hole thermodynamics.

**12 December 2023, 14:00**

I introduce a new class of defects in conformal field theory (CFT), termed orientifold defects. These defects arise from quotienting the spacetime by a Z_2 automorphism, and provide higher-codimension generalizations of CFT on a real projective space (RP_d). The orientifold defects of codimension-p preserve the SO(d-p-1)xSO(p) subgroup of the conformal group, and the two-point functions of local operators in their presence satisfy the orientifold crossing equation, which we present. In contrast to standard conformal defects, both channels of the crossing equation involve bulk operators only, and operators localized on the defect are absent. I will then present a classification of half-BPS orientifold defects in N=4 SYM and provide evidence that they preserve integrability of planar N=4 SYM and are holographic dual to orientifolds in type IIB string theory on AdS_5 times S^5.

**5 December 2023, 14:00**