We use the Fuzzy Sphere technology to extract new 3d Ising CFT data and examine its properties in light of expectations from ergodicity.  In our analysis, a microscopic construction of the special conformal generators plays an important role.  We also study 3d Ising Field Theory, namely, the Ising CFT deformed by a relevant operator.   Here we use both the  Fuzzy Sphere directly, as well as Hamiltonian truncation employing the new Ising CFT data.
 
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We consider « fool’s crowns » — parts of Riemann surfaces with holes with n marked points/bordered cusps on a hole boundary decorated by horocycles. We define volumes of the corresponding moduli spaces by postulating a decoration-independent action, which in the limit of n tending to infinity transforms into a Schwarzian action on boundary « trumpets ». We derive the corresponding volumes for arbitrary n and coupling constant kappa and describe the statistical model obtained in terms of Brownian bridges. This is a joint work with Timothy Budd (Nijmegen Univ.)
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Infrared divergences obscure key analytic properties of scattering amplitudes, exposing gaps in our understanding of unitarity, causality, and crossing symmetry in theories with long-range forces. In this talk, I will use a simple model to illustrate novel analytic features of long-range theories, including modifications to the connectedness structure of amplitudes and to the general optical theorem. Since the LSZ reduction formula does not apply to theories with long-range forces, I will also present a modified version of LSZ reduction for this model, which accounts for long-range interactions and yields IR-finite amplitudes without ambiguous scales or ill-defined integrals.
 
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Séminaire d’Analyse
The bispectral problem concerns the construction and the classification of operators possessing a symmetry between the space and spectral variables. Different versions of this problem have interesting connections to several areas of mathematics such as integrable systems, algebraic geometry, representation theory, classical orthogonal polynomials, etc. I will review the problem and some of these connections, and then discuss recent results related to quantum integrable systems and hypergeometric functions associated with several classical multivariate distributions.
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
I will present the detailed construction of an extension of the Bondi framework which includes a non-vanishing twist, i.e. the relaxation of the hyperspace-orthogonality condition. This extension has several advantages which have been noted in recent work. First, it allows to access a Carroll-covariant structure on Scri. Second, and most importantly, the presence of a non-vanishing twist allows to write all the algebraically special solutions in finite form. This includes for example Kerr or supertranslated Schwarzschild, which would otherwise require an infinite 1/r expansion when written in the standard non-twisting Bondi gauge. This opens the possibility of defining symplectic symmetries for these algebraically special solutions. The construction of the algebraically general solutions near null infinity requires the use of a combination of the Newman-Penrose and metric formalisms, which will be presented in detail.
 
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Séminaire de géométrie arithmétique
Let k be a perfect field of characteristic p > 0. The Hodge-Witt sheaf is a sheaf with transfer on the category of smooth k-varieties. However, since it does not satisfy the cohomological A1-invariance, the Hodge-Witt cohomology is not representable in Voevodsky’s category of motives. One way to overcome this drawback is to consider the category of motives with modulus defined by Kahn-Miyazaki-Saito-Yamazaki. We define the Hodge-Witt sheaf for modulus pairs over k satisfying the properties called the cohomological cube invariance and the cohomological blow-up invariance. These imply that the Hodge-Witt cohomology is representable in the category of motives with modulus under resolution of singularities. Also, we try to discuss properties of our Hodge-Witt sheaves for modulus pairs and possible relationship with another construction by Ren-Rulling. This is partly joint work in progress with Veronika Ertl. 
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Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

The modular bootstrap has been a powerful tool for carving out the landscape of allowed two-dimensional conformal field theories (CFTs).  In this talk, I describe a complementary approach to standard modular bootstrap bounds: using modern machine learning strategies to actively search for CFT spectra that yield a valid torus partition function.  Using insights from statistical inference and a custom singular-value-based optimizer, I present evidence for an obstruction to finding CFTs with small central charge and large spectral gaps, and I speculate on what this might imply for the structure of the CFT landscape.  Along the way, I reflect on « centaur » approaches to theoretical physics, where human physicists and artificial intelligence collaborate to explore spaces of theories that would be difficult to navigate alone.
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
I will study planar, maximally supersymmetric 4d EFTs that reduce to ${mathcal N} = 4$ SYM at low energies and show that novel constraints arise from the six-point amplitude. By constructing the six-scalar amplitude and imposing supersymmetry together with standard tree-level factorization, assuming parity-even scalar contact terms, I find striking nonlinear relations among the four-point Wilson coefficients. These relations collapse much of the naive EFT parameter space. When combined with positivity bounds from unitarity and causality, the allowed region in Wilson-coefficient space shrinks to a thin sliver converging on the open-superstring Veneziano amplitude, strongly suggesting that maximal supersymmetry singles out the tree-level string answer. More broadly, the result shows that higher-point amplitudes contain qualitatively new bounds on the space of EFTs, and that the space of consistent quantum field theories may be much smaller than current four-point analyses suggest.
 
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Séminaire d’Analyse
Motivated by the phenomenon of duality for interacting particle systems we introduce two classes of Pfaffian kernels describing a number of Pfaffian point processes in the « bulk » and at the « edge ». Using the probabilistic method due to Mark Kac, we prove two  Szegő-type asymptotic expansion theorems for the corresponding Fredholm Pfaffians. The idea of the proof is to introduce an effective random walk with transition density determined by the Pfaffian kernel, express the logarithm of the Fredholm Pfaffian through expectations with respect to the random walk, and analyse the expectations using general results on random walks. We demonstrate the utility of the theorems by calculating asymptotics for the empty interval and non-crossing probabilities for a number of examples of Pfaffian point processes: coalescing/annihilating Brownian motions, massive coalescing Brownian motions, real zeros of Gaussian power series and Kac polynomials, and real eigenvalues for the real Ginibre ensemble. (Joint work with Will FitzGerald and Roger Tribe.)
 
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