We introduce a category of inscribed v-sheaves as a minimal differential extension of the theory of diamonds in p-adic geometry, then explain how to apply this theory to differentiate natural period maps in p-adic Hodge theory.
 
========
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.

In classical work, Bowen and Margulis proved the equidistribution of closed geodesics in any closed hyperbolic manifold. Together with Jeremy Kahn and Vladimir Marković, we asked ourselves what happens in a 3-manifold if we replace curves by surfaces. (Slightly different aspects of this question have also been studied by Calegari, Marques and Neves.) The natural analogue of a closed geodesic is then a minimal surface, as totally geodesic surfaces exist only very rarely. Nevertheless, it still makes sense (for various reasons, in particular to ensure uniqueness of the minimal representative) to restrict our attention to surfaces that are almost totally geodesic.
The statistics of these surfaces then depend very strongly on how we order them: by genus, or by area. If we focus on surfaces whose area tends to infinity, we conjecture that they do indeed equidistribute; we proved a partial result in this direction. If, however, we focus on surfaces whose genus tends to infinity, the situation is completely opposite: we proved that they then accumulate onto the totally geodesic surfaces of the manifold (if there are any).
 

We review some results and questions concerning sparse equidistribution results for horocycle flows in constant curvature, and present a recent result joint with Kanigowski and Radziwill that horocycle flows equidistribute for all points with infinite discrete orbit along times equal to products of two primes.
 

Séminaire de géométrie arithmétique
The universal Weil cohomology (obtained in a recent work jointly with B. Kahn) is taking values in an abelian Q-linear (Q is the field of rational numbers) tensor category M which is rigid but its Q-algebra E = End (1) of endomorphisms of the unit is not a field, a priori. André’s theory of motivated cycles MA, in characteristic zero, can be recovered via the universal Weil cohomology as a localisation of M; thus E = Q  if and only if M = MA is André’s category which is then universal for all Weil cohomologies taking values in abelian Q-linear rigid tensor categories. A similar picture holds true for the universal mixed Weil cohomology with values in MM with respect to Nori motives NM.
However, in any characteristic, this new Weil cohomology yields a universal homological equivalence hum and a canonical comparison faithful tensor functor F from Grothendieck motives (modulo hum) MG to M. This F is an equivalence if and only if MG is abelian, F is exact and the Grothendieck Lefschetz standard conjecture holds true. Moreover, F is an equivalence with M semi-simple if and only if hum is numerical equivalence. Therefore Grothendieck’s standard conjectures for the universal Weil cohomology or the stronger Voevodsky’s nilpotence conjecture (independently of any Weil cohomology) imply that E = Q.
 A standard hypothesis is then that this absolutely flat Q-algebra E is a domain hence a field. This hypothesis is equivalent to the property that M is Tannakian. Similarly, for MM. Note that, for every self correspondence, the trace and the Lefschetz number (as well as the coefficients of the characteristic polynomials) are defined over E. As a consequence, if E is a field all these are the same independently of the Weil cohomology.
========
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 Effective Field Theories that can originate from microscopic unitary theories, and their relation to moment theory. I will show that  theories with isolated massive higher-spin particles, and theories with very irrelevant interactions, don’t posses healthy UV completions, and I will show how Vector Meson Dominance follows from such first principles.
 
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.

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.