Probability and analysis informal seminar
Schwarzian Theory is a quantum field theory which has attracted a lot of attention in the physics literature in the context of two-dimensional quantum gravity, black holes and AdS/CFT correspondence. It is predicted to be universal and arise in many systems with emerging conformal symmetry, most notably in Sachdev–Ye–Kitaev random matrix model and Jackie–Teitelboim gravity.In this talk we will discuss our recent progress on developing rigorous mathematical foundations of the Schwarzian Field Theory, including rigorous construction of the corresponding measure, calculation of both the partition function and a natural class of correlation functions, and a large deviation principle.
 
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

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.
 
 
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

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.
 
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

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.
 
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

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.  
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

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. 
 
 
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Au niveau microscopique, un gaz est une collection de particules neutres en interaction. Le très grand nombre de degrés de libertés et la sensibilité du système à de très petites perturbations font qu’il est essentiellement impossible d’en prédire la dynamique de façon déterministe.
A la fin du XIXème siècle, Boltzmann a proposé de décrire le comportement du gaz de façon alternative par une approche statistique. Une question naturelle est alors de savoir si l’hypothèse d’indépendance statistique qui sous-tend ce modèle est compatible avec la dynamique microscopique et en quel sens l’équation de Boltzmann en est une bonne approximation.
Ce cours donnera quelques éléments de réponse à cette question, dans le cadre simplifié d’interactions par contact.
1. L’équation de Boltzmann, l’hypothèse de chaos et le théorème H
2. Loi des grands nombres pour la dynamique des sphères dures
3. Corrélations, clusters dynamiques
4. Fluctuations et grandes déviations pour la dynamique des sphères dures
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
At the microscopic level, a gas is a collection of interacting neutral particles. The very large number of degrees of freedom and the sensitivity of the system to very small perturbations mean that it is essentially impossible to predict its dynamics deterministically.
At the end of the 19th century, Boltzmann proposed describing the behaviour of gas in an alternative way, using a statistical approach. A natural question is whether the assumption of statistical independence that underlies this model is compatible with microscopic dynamics and in what sense the Boltzmann equation is a good approximation.
This course will provide some answers to this question, within the simplified framework of contact interactions.
1. The Boltzmann equation, the chaos hypothesis and the H theorem
2. Law of large numbers for the dynamics of hard spheres
3. Correlations, dynamic clusters
4. Fluctuations and large deviations for the dynamics of hard spheres
 

Au niveau microscopique, un gaz est une collection de particules neutres en interaction. Le très grand nombre de degrés de libertés et la sensibilité du système à de très petites perturbations font qu’il est essentiellement impossible d’en prédire la dynamique de façon déterministe.
A la fin du XIXème siècle, Boltzmann a proposé de décrire le comportement du gaz de façon alternative par une approche statistique. Une question naturelle est alors de savoir si l’hypothèse d’indépendance statistique qui sous-tend ce modèle est compatible avec la dynamique microscopique et en quel sens l’équation de Boltzmann en est une bonne approximation.
Ce cours donnera quelques éléments de réponse à cette question, dans le cadre simplifié d’interactions par contact.
1. L’équation de Boltzmann, l’hypothèse de chaos et le théorème H
2. Loi des grands nombres pour la dynamique des sphères dures
3. Corrélations, clusters dynamiques
4. Fluctuations et grandes déviations pour la dynamique des sphères dures
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
At the microscopic level, a gas is a collection of interacting neutral particles. The very large number of degrees of freedom and the sensitivity of the system to very small perturbations mean that it is essentially impossible to predict its dynamics deterministically.
At the end of the 19th century, Boltzmann proposed describing the behaviour of gas in an alternative way, using a statistical approach. A natural question is whether the assumption of statistical independence that underlies this model is compatible with microscopic dynamics and in what sense the Boltzmann equation is a good approximation.
This course will provide some answers to this question, within the simplified framework of contact interactions.
1. The Boltzmann equation, the chaos hypothesis and the H theorem
2. Law of large numbers for the dynamics of hard spheres
3. Correlations, dynamic clusters
4. Fluctuations and large deviations for the dynamics of hard spheres
 

Au niveau microscopique, un gaz est une collection de particules neutres en interaction. Le très grand nombre de degrés de libertés et la sensibilité du système à de très petites perturbations font qu’il est essentiellement impossible d’en prédire la dynamique de façon déterministe.
A la fin du XIXème siècle, Boltzmann a proposé de décrire le comportement du gaz de façon alternative par une approche statistique. Une question naturelle est alors de savoir si l’hypothèse d’indépendance statistique qui sous-tend ce modèle est compatible avec la dynamique microscopique et en quel sens l’équation de Boltzmann en est une bonne approximation.
Ce cours donnera quelques éléments de réponse à cette question, dans le cadre simplifié d’interactions par contact.
1. L’équation de Boltzmann, l’hypothèse de chaos et le théorème H
2. Loi des grands nombres pour la dynamique des sphères dures
3. Corrélations, clusters dynamiques
4. Fluctuations et grandes déviations pour la dynamique des sphères dures
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
At the microscopic level, a gas is a collection of interacting neutral particles. The very large number of degrees of freedom and the sensitivity of the system to very small perturbations mean that it is essentially impossible to predict its dynamics deterministically.
At the end of the 19th century, Boltzmann proposed describing the behaviour of gas in an alternative way, using a statistical approach. A natural question is whether the assumption of statistical independence that underlies this model is compatible with microscopic dynamics and in what sense the Boltzmann equation is a good approximation.
This course will provide some answers to this question, within the simplified framework of contact interactions.
1. The Boltzmann equation, the chaos hypothesis and the H theorem
2. Law of large numbers for the dynamics of hard spheres
3. Correlations, dynamic clusters
4. Fluctuations and large deviations for the dynamics of hard spheres
 

Au niveau microscopique, un gaz est une collection de particules neutres en interaction. Le très grand nombre de degrés de libertés et la sensibilité du système à de très petites perturbations font qu’il est essentiellement impossible d’en prédire la dynamique de façon déterministe.
A la fin du XIXème siècle, Boltzmann a proposé de décrire le comportement du gaz de façon alternative par une approche statistique. Une question naturelle est alors de savoir si l’hypothèse d’indépendance statistique qui sous-tend ce modèle est compatible avec la dynamique microscopique et en quel sens l’équation de Boltzmann en est une bonne approximation.
Ce cours donnera quelques éléments de réponse à cette question, dans le cadre simplifié d’interactions par contact.
1. L’équation de Boltzmann, l’hypothèse de chaos et le théorème H
2. Loi des grands nombres pour la dynamique des sphères dures
3. Corrélations, clusters dynamiques
4. Fluctuations et grandes déviations pour la dynamique des sphères dures
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
At the microscopic level, a gas is a collection of interacting neutral particles. The very large number of degrees of freedom and the sensitivity of the system to very small perturbations mean that it is essentially impossible to predict its dynamics deterministically.
At the end of the 19th century, Boltzmann proposed describing the behaviour of gas in an alternative way, using a statistical approach. A natural question is whether the assumption of statistical independence that underlies this model is compatible with microscopic dynamics and in what sense the Boltzmann equation is a good approximation.
This course will provide some answers to this question, within the simplified framework of contact interactions.
1. The Boltzmann equation, the chaos hypothesis and the H theorem
2. Law of large numbers for the dynamics of hard spheres
3. Correlations, dynamic clusters
4. Fluctuations and large deviations for the dynamics of hard spheres