The Symmetry Topological Field Theory (SymTFT) is a realization of the philosophy that symmetries in Quantum Field Theory (QFT) can be studied using tools from Topological Quantum Field Theory (TQFT). In this talk, I will introduce this topic and motivate the construction of the SymTFT for a d-dimensional QFT as a (d+1)-dimensional topological field theory. I will explain how this (d+1)-dimensional theory is completely determined by the global symmetries of the d-dimensional QFT, making it « universal » for all d-dimensional theories sharing the same symmetries. A significant advantage of the SymTFT is its ability to separate kinematical aspects from dynamical ones. This separation enables the analysis of the constraints imposed by a given symmetry structure on the dynamics, with a prime example being ‘t Hooft anomalies, using only TQFT tools and observables.
 
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
We consider linear perturbations around the Schwarzschild black hole in four dimensions. We describe two methods that provide the quantization condition for the quasinormal mode frequencies of the perturbation field. The first method is based on techniques from supersymmetric gauge theory and conformal field theory that allow to explicitly write the connection coefficients for the differential equation encoding the spectral problem. The second method is based on a small-frequency expansion of the solutions of the differential equation, and permits to obtain the corresponding expansion for the elements of the scattering matrix, which have poles in the quasinormal mode frequencies. The relations between the two approaches will be discussed, together with the respective advantages.
 
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We consider certain representations of a surface group into PGL(4,R) called convex cocompact coaffine representations. These representations act geometrically on a 3-dimensional convex body in projective space, and are part of a broader (and more difficult) landscape of such geometric actions. From classical cases, we would anticipate an analytic object called a transverse measured lamination to capture the geometry of these representations, however paradoxical examples reveal that a generalization is necessary. We will discuss a nice resolution to these difficulties, and describe a space of affine measured laminations which parametrize the space of convex cocompact coaffine representations. Along the way we make an interesting connection to the dynamics of affine interval exchange transformations. Joint work with James Farre.
 

For divergent sequences of Schottky groups of the N-dimensional hyperbolic space HN, the Hausdorff dimension of the limit sets typically goes to zero. By considering actions of these groups on the infinite-dimensional hyperbolic space, we give an asymptotic for this convergence.
This is joint work with Gilles Courtois. It is partly inspired by recent work of Dang-Mehmeti. If time permits, I will compare the two approaches.
 

Séminaire de géométrie arithmétique
Pro-étale cohomology of rigid-analytic varieties over the p-adic complex numbers has surprising features, which can be explained by calculating the pro-étale cohomology via quasi-coherent sheaves on the Fargues-Fontaine curve. In this talk I want to explain the recent construction of a 6-functor formalism with values in quasi-coherent sheaves on the Fargues-Fontaine curve, and to discuss some of its properties. This is joint work with Arthur-César Le Bras and Lucas Mann.
 
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I will discuss the dynamics of 2d gauge theories with massless adjoint matter, focusing on scenarios where the theory flows to a non-trivial gapless fixed point. Specifically, I will examine the case of an SU(N) gauge theory coupled to an adjoint Dirac fermion, which is conjectured to flow to a WZW coset model. I will argue that this IR CFT is subtle enough to capture interesting features essential for understanding the (de)confinement mechanisms in gauge theories. While the massless model is gapless and deconfined, I will discuss the conditions under which the theory flows to a gapped confined phase when a mass for the adjoint matter is introduced, showing how this can be predicted by analyzing the intricate symmetry structure of the CFT. Finally, I will use these insights to compute the behavior of the tension of confining strings and comment on how this quantity varies across the massive phase diagram, reaching both known and novel behaviors in specific limits.  
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Séminaire de géométrie arithmétique
In the setting of algebraic geometry in characteristic zero (or of complex geometry), the Bernstein-Sato polynomial is a polynomial defined for a function on a smooth variety and has deep connections with several invariants attached to the singularities of the zero locus of the function, among which the focus in the talk is on the connection with the monodromy eigenvalues on the nearby cycle sheaf, known as the theorem of Kashiwara and Malgrange. 
There have been attempts to develop a Bernstein-Sato-type theory also in the setting of positive characteristic, and these have led to a definition of Bernstein-Sato roots (but not their multiplicities), which again has deep connections to the theory of singularities. However, it has not been well studied how this theory is related to the monodromy eigenvalues on a nearby cycle sheaf. In this talk, I will explain an observation that the Bernstein-Sato roots seem to recover some of the monodromy eigenvalues on a suitable nearby cycle sheaf but only those on the unit root part, which we think suggests a better definition of Bernstein-Sato roots that captures all the monodromy eigenvalues and produces finer information about the singularities of the zero locus. This is a joint work in progress with Eamon Quinlan-Gallego and Daichi Takeuchi. 
 
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Recent advances in modelling unbound binary black hole interactions have been driven by the application of scattering amplitude methods to generate results within the post-Minkowskian (PM) expansion. However, this expansion breaks down when approaching the strong-field where the large curvature effects become non-negligible. In this talk, I will show how numerical information from self-force (SF), an expansion in the small mass ratio of the system, can inform higher-order coefficients in the PM expansion. I will also show how a single point of SF scattering data can be used to resum the PM series, providing accurate predictions for scattering angles across all separations. Additionally, I will present results from unbound numerical relativity simulations, where the full Einstein field equations are solved for comparable mass systems, and compare these with predictions from PM-informed effective one body models.
 
 
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Probability and analysis informal seminar
We start by reviewing the classical Sherrington-Kirkpatrick (SK) model. In this model, +1/-1-valued spins interact with each other subject to random coupling constants. The covariance of the random interaction is quadratic in terms of spin overlaps. Parisi proposed the celebrated variational formula for the limit of free energy of the SK model in the 80s, which was later rigorously verified in the works by Guerra and Talagrand. This formula has been generalized in various settings, for instance, to vector-valued spins, by Panchenko. However, in these cases, the convexity of the interaction is crucial. In general, the limit of free energy in non-convex models is not known and we do not have variational formulas as valid candidates. Here, we report recent progress through the lens of the Hamilton-Jacobi equation. Under the assumption that the limit of free energy exists, we show that the value of the limit is prescribed by a characteristic line; and the limit (as a function) satisfies an infinite-dimensional Hamilton-Jacobi equation « almost everywhere ». This talk is based on a joint work with Jean-Christophe Mourrat.​
 
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In this talk, we bootstrap various objects in planar maximally supersymmetric Yang- Mills theory. Focusing on the four-point correlation function of stress-tensor, we first demonstrate why the conventional bootstrap approach fails and new techniques are required. Next, we introduce a set of sum rules that are tailored for this problem as they are sensitive only to single-traces in the OPE expansion. Integrability enters at this stage and provides information on the spectrum of these operators. Their OPE coefficients, however, remain elusive. We then discuss how these sum rules can be employed in numerical bootstrap to nonperturbatively bound the OPE coefficients, the four-point correlation function and the energy-energy correlator. We show, for the first time, rigorous non-perturbative results for the planar OPE coefficient of single-trace operators as well as the correlation function at various points in cross-ratio space. Additionally, focusing on the energy-energy correlator (EEC), we present rigorous bounds for its spin 2 and spin 3 Legendre coefficients as well as the full EEC function at various angles. These results were obtained for a wide range of  t’Hooft couplings, highlighting the power of the bootstrap in probing non-perturbative aspects of planar N=4 SYM theory.
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
In conventional world-line formalism for spinning binaries in general relativity, one assumes that the dynamical degrees of freedom for spin are the completely captured by the rest frame canonical spin. A spin supplementary condition (SSC) is then necessary to remove redundancies. We study this problem from an amplitude-based field theory perspective. In higher spin field theories, it is notoriously difficult to impose transverse and traceless conditions when interactions are included. We take an alternative approach and keep the additional degrees of freedom. We see that for generic Wilson coefficients, we obtain a system with a dynamical mass dipole that has physical effect starting at the quadrupole level. It will decouple when we choose special values for Wilson coefficients, and we land back on the dynamics of conventional spinning binaries. The situation is very similar to a symmetry breaking in the classical limit. We also construct a world-line Lagrangian and a classical effective Hamiltonian that completely match the physics mentioned above, which incorporates a dynamical mass dipole as the additional dynamical degree of freedom. The mass dipole has physical effects, and its significance is a question for phenomenology. On the other hand, the dipole can be removed by an emergent world-line shift symmetry when Wilson coefficients take special values. From this perspective, our formalism can simplify the calculation for conventional spinning binaries, as the SSC constraint can be effectively relaxed.
 
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Given a compact hyperbolic surface together with a suitable choice of orthonormal basis of Laplace eigenforms, one can consider two natural spectral invariants: 1) the Laplace spectrum $Lambda$, and 2) the 3-tensor Cijk representing pointwise multiplication (as a densely defined map L2 x L2  $to$ L2) in the given basis. Which pairs ($Lambda$,C) arise this way? Both $Lambda$ and C are highly transcendental objects. Nevertheless, we will give a concrete and almost completely algebraic answer to this question, by writing down necessary and sufficient conditions in the form of equations satisfied by the Laplace eigenvalues and the Cijk. This answer was suggested by physicists Kravchuk, Mazac, and Pal, who introduced these equations (in an equivalent form) as a rigorous model for the crossing equations in conformal field theory.
 
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